Saturday, 12 October 2013

Partial derivative: CH:5 IN ENGINEERING


In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
The partial derivative of a function f with respect to the variable x is variously denoted by
f^\prime_x,\ f_x,\ \partial_x f, \text{ or } \frac{\partial f}{\partial x}
The partial-derivative symbol is ∂. One of the first known uses of the symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences. The modern partial derivative notation is by Adrien-Marie Legendre (1786), though he later abandoned it; Carl Gustav Jacob Jacobi re-introduced the symbol in 1841

Introduction: 


Suppose that ƒ is a function of more than one variable. For instance,
z = f(x,y) = \,\! x^2 + xy + y^2.\,

 

The graph of this function defines a surface in Euclidean space. To every point on this surface, there are an infinite number of tangent lines. Partial differentiation is the act of choosing one of these lines and finding its slope. Usually, the lines of most interest are those that are parallel to the xz-plane, and those that are parallel to the yz-plane (which result from holding either y or x constant, respectively.)
To find the slope of the line tangent to the function at P(1, 1, 3) that is parallel to the xz-plane, the y variable is treated as constant. The graph and this plane are shown on the right. On the graph below it, we see the way the function looks on the plane y = 1. By finding the derivative of the equation while assuming that y is a constant, the slope of ƒ at the point (x, y, z) is found to be:

\frac{\partial z}{\partial x} = 2x+y
So at (1, 1, 3), by substitution, the slope is 3. Therefore
\frac{\partial z}{\partial x} = 3
at the point. (1, 1, 3). That is, the partial derivative of z with respect to x at (1, 1, 3) is 3.


Definition:

Basic definition,

The function f can be reinterpreted as a family of functions of one variable indexed by the other variables:
f(x,y) = f_x(y) = \,\! x^2 + xy + y^2.\,
In other words, every value of x defines a function, denoted fx, which is a function of one variable.[2] That is,
f_x(y) = x^2 + xy + y^2.\,
Once a value of x is chosen, say a, then f(x,y) determines a function fa which sends y to a2 + ay + y2:
f_a(y) = a^2 + ay + y^2. \,
In this expression, a is a constant, not a variable, so fa is a function of only one real variable, that being y. Consequently, the definition of the derivative for a function of one variable applies:
f_a'(y) = a + 2y. \,
The above procedure can be performed for any choice of a. Assembling the derivatives together into a function gives a function which describes the variation of f in the y direction:
\frac{\partial f}{\partial y}(x,y) = x + 2y.\,
This is the partial derivative of f with respect to y. Here ∂ is a rounded d called the partial derivative symbol. To distinguish it from the letter d, ∂ is sometimes pronounced "del" or "partial" instead of "dee".
In general, the partial derivative of a function f(x1,...,xn) in the direction xi at the point (a1,...,an) is defined to be:
\frac{\partial f}{\partial x_i}(a_1,\ldots,a_n) = \lim_{h \to 0}\frac{f(a_1,\ldots,a_i+h,\ldots,a_n) - f(a_1,\ldots, a_i, \dots,a_n)}{h}.
In the above difference quotient, all the variables except xi are held fixed. That choice of fixed values determines a function of one variable f_{a_1,\ldots,a_{i-1},a_{i+1},\ldots,a_n}(x_i) = f(a_1,\ldots,a_{i-1},x_i,a_{i+1},\ldots,a_n), and by definition,
\frac{df_{a_1,\ldots,a_{i-1},a_{i+1},\ldots,a_n}}{dx_i}(a_i) = \frac{\partial f}{\partial x_i}(a_1,\ldots,a_n).
In other words, the different choices of a index a family of one-variable functions just as in the example above. This expression also shows that the computation of partial derivatives reduces to the computation of one-variable derivatives.
An important example of a function of several variables is the case of a scalar-valued function f(x1,...xn) on a domain in Euclidean space Rn (e.g., on R2 or R3). In this case f has a partial derivative ∂f/∂xj with respect to each variable xj. At the point a, these partial derivatives define the vector
\nabla f(a) = \left(\frac{\partial f}{\partial x_1}(a), \ldots, \frac{\partial f}{\partial x_n}(a)\right).
This vector is called the gradient of f at a. If f is differentiable at every point in some domain, then the gradient is a vector-valued function ∇f which takes the point a to the vector ∇f(a). Consequently, the gradient produces a vector field.
A common abuse of notation is to define the del operator (∇) as follows in three-dimensional Euclidean space R3 with unit vectors \mathbf{\hat{i}}, \mathbf{\hat{j}}, \mathbf{\hat{k}}:
\nabla = \bigg[{\frac{\partial}{\partial x}} \bigg] \mathbf{\hat{i}} + \bigg[{\frac{\partial}{\partial y}}\bigg] \mathbf{\hat{j}} + \bigg[{\frac{\partial}{\partial z}}\bigg] \mathbf{\hat{k}}
Or, more generally, for n-dimensional Euclidean space Rn with coordinates (x1, x2, x3,...,xn) and unit vectors (\mathbf{\hat{e}_1}, \mathbf{\hat{e}_2}, \mathbf{\hat{e}_3}, \dots , \mathbf{\hat{e}_n}):
\nabla = \sum_{j=1}^n \bigg[{\frac{\partial}{\partial x_j}}\bigg] \mathbf{\hat{e}_j} = \bigg[{\frac{\partial}{\partial x_1}}\bigg] \mathbf{\hat{e}_1} + \bigg[{\frac{\partial}{\partial x_2}}\bigg] \mathbf{\hat{e}_2} + \bigg[{\frac{\partial}{\partial x_3}}\bigg] \mathbf{\hat{e}_3} + \dots + \bigg[{\frac{\partial}{\partial x_n}}\bigg] \mathbf{\hat{e}_n}

Formal definition

Like ordinary derivatives, the partial derivative is defined as a limit. Let U be an open subset of Rn and f : U → R a function. The partial derivative of f at the point a = (a1, ..., an) ∈ U with respect to the i-th variable ai is defined as
\frac{ \partial }{\partial a_i }f(\mathbf{a}) = \lim_{h \rightarrow 0}{ f(a_1, \dots , a_{i-1}, a_i+h, a_{i+1}, \dots ,a_n) - f(a_1, \dots, a_i, \dots ,a_n) \over h }
Even if all partial derivatives ∂f/∂ai(a) exist at a given point a, the function need not be continuous there. However, if all partial derivatives exist in a neighborhood of a and are continuous there, then f is totally differentiable in that neighborhood and the total derivative is continuous. In this case, it is said that f is a C1 function. This can be used to generalize for vector valued functions (f : U → R'm) by carefully using a componentwise argument.
The partial derivative \frac{\partial f}{\partial x} can be seen as another function defined on U and can again be partially differentiated. If all mixed second order partial derivatives are continuous at a point (or on a set), f is termed a C2 function at that point (or on that set); in this case, the partial derivatives can be exchanged by Clairaut's theorem:

\frac{\partial^2f}{\partial x_i\, \partial x_j} = \frac{\partial^2f} {\partial x_j\, \partial x_i}. 

Examples:

The volume V of a cone depends on the cone's height h and its radius r according to the formula
V(r, h) = \frac{\pi r^2 h}{3}.
The partial derivative of V with respect to r is
\frac{ \partial V}{\partial r} = \frac{ 2 \pi r h}{3},
which represents the rate with which a cone's volume changes if its radius is varied and its height is kept constant. The partial derivative with respect to h is
\frac{ \partial V}{\partial h} = \frac{\pi r^2}{3},
which represents the rate with which the volume changes if its height is varied and its radius is kept constant.
By contrast, the total derivative of V with respect to r and h are respectively
\frac{\operatorname dV}{\operatorname dr} = \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r} + \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h}\frac{\operatorname d h}{\operatorname d r}
and
\frac{\operatorname dV}{\operatorname dh} = \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h} + \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r}\frac{\operatorname d r}{\operatorname d h}
The difference between the total and partial derivative is the elimination of indirect dependencies between variables in partial derivatives.
If (for some arbitrary reason) the cone's proportions have to stay the same, and the height and radius are in a fixed ratio k,
k = \frac{h}{r} = \frac{\operatorname d h}{\operatorname d r}.
This gives the total derivative with respect to r:
\frac{\operatorname dV}{\operatorname dr} = \frac{2 \pi r h}{3} + \frac{\pi r^2}{3}k
Which simplifies to:
\frac{\operatorname dV}{\operatorname dr} = k\pi r^2
Similarly, the total derivative with respect to h is:
\frac{\operatorname dV}{\operatorname dh} = \pi r^2
Equations involving an unknown function's partial derivatives are called partial differential equations and are common in physics, engineering, and other sciences and applied disciplines.




Notation:

For the following examples, let f be a function in x, y and z.
First-order partial derivatives:
\frac{ \partial f}{ \partial x} = f_x = \partial_x f.
Second-order partial derivatives:
\frac{ \partial^2 f}{ \partial x^2} = f_{xx} = \partial_{xx} f.
Second-order mixed derivatives:
\frac{\partial^2 f}{\partial y \, \partial x} = \frac{\partial}{\partial y} \left( \frac{\partial f}{\partial x} \right) = (f_{x})_{y} = f_{xy} = \partial_{yx} f.
Higher-order partial and mixed derivatives:
\frac{ \partial^{i+j+k} f}{ \partial x^i\, \partial y^j\, \partial z^k } = f^{(i, j, k)}.
When dealing with functions of multiple variables, some of these variables may be related to each other, and it may be necessary to specify explicitly which variables are being held constant. In fields such as statistical mechanics, the partial derivative of f with respect to x, holding y and z constant, is often expressed as

\left( \frac{\partial f}{\partial x} \right)_{y,z}. 

Antiderivative analogue:

There is a concept for partial derivatives that is analogous to antiderivatives for regular derivatives. Given a partial derivative, it allows for the partial recovery of the original function.
Consider the example of \frac{\partial z}{\partial x} = 2x+y. The "partial" integral can be taken with respect to x (treating y as constant, in a similar manner to partial derivation):
z = \int \frac{\partial z}{\partial x} \,dx = x^2 + xy + g(y)
Here, the "constant" of integration is no longer a constant, but instead a function of all the variables of the original function except x. The reason for this is that all the other variables are treated as constant when taking the partial derivative, so any function which does not involve x will disappear when taking the partial derivative, and we have to account for this when we take the antiderivative. The most general way to represent this is to have the "constant" represent an unknown function of all the other variables.
Thus the set of functions x^2 + xy + g(y), where g is any one-argument function, represents the entire set of functions in variables x,y that could have produced the x-partial derivative 2x+y.
If all the partial derivatives of a function are known (for example, with the gradient), then the antiderivatives can be matched via the above process to reconstruct the original function up to a constant

 

 


 

 

 



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HELLO EVERYBODY
I AM SHAIKH SHAHEZAD , I LIVE IN RAIKHAD,I COMPLETED MY H.S.C.&S.S.C FROM ST.XAVIERS HIGH SCHOOL MIRZAPUR FROM GSEB. I STUDYING IN IT ENGINEERING IN HASMUKH GOSWAMI COLLEGE OF ENGINEERING VAHELAL AFFILIATED WITH GUJRAT UNIVERSITY . MY FATHER NAME IS SHAIKH SAJIDBHAI AND MY MOTHER NAME IS SHAIKH SHAHINABANU. I LIKE TO PLAY FOOTBALL,I GOT THE PRIZES FOR SCIENCE PROJECT AT THE STATE LEVEL AND GOT THE AWARD FOR DRAWING COMPETION. MY AIM TO BECOME A SUCCESFUL AND FAMOUS SOFTWARE ENGINEERI HAVE STRONG FEELING MY DREAMS WILL BECOME TRUE.
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Samsung Galaxy Tab 3 311 review:

When one thinks about purchasing an Android tablet, then choosing one is not an easy task. Buyers are spoilt for choice in terms of form factor, features and more importantly price. Of course, when one homes in on the sub-10-inch form-factor, the Google Nexus 7 becomes an obvious choice, but this year Samsung has also brought its Galaxy Tab 3 311 to the table flush with the new Galaxy S4 design language. With the Galaxy Tab 3 311 being able to double up as a phone as well, the Nexus 7 does not remain an obvious choice for a premium sub-10-inch Android tablet. That said, in typical Samsung fashion the user needs to deal with certain Samsung specific idiosyncrasies and the fact the Galaxy Tab 3 311 does not provide the top-of-the-line specsheet is a bummer. However, as always one does not judge a book by its cover and we ran the device through our test hoops. Read on to find out how it fared.

Design:

 

Samsung has now established an unified design language across its products, which filters through even to the Galaxy Tab 3 311. So, elements like a glossy hyper-glaze chassis and a faux chrome spine is retained in the Galaxy Tab 3 311 akin to recent smartphones like the Galaxy S4 and the Galaxy Mega. The main advantage of this industrial design is that Samsung is able to keep the tablet incredibly thin at 7.4mm and it weighs only 314 grams. Additionally, Samsung has shaved off the bezel on the screen to such a degree that one feels this more of 7-inch tablet than an 8-incher. All these little figures mean that the Galaxy Tab 3 is ergonomically delightful to use with one-hand, something which cannot be said about sub-10-inch tablets from other OEMs, save for the iPad mini.

The biggest disadvantage of this design is that it feels cheap and when compared to the iPad mini or even the Nexus 7. The build quality falls short of one’s expectations in a product at this price bracket. The plastic exudes a slimy and slippery feel to it, but at the same time this very plastic has proven to be quite durable to dents and scratches when compared to metallic finishes seen on the iPad mini.
Like most modern devices, the front highlights the large Super AMOLED display which has a resolution of 1280×800 pixels. Below the display, we have the three Android keys, arranged in Samsung’s traditional style, with a large pill shaped home key in the centre. Above the screen, one finds a front-facing camera and the regular arrangement of sensors.


As this device also boasts voice calling capabilities, the left spine houses a micro SIM slot which is covered by a flip-out door. Additionally, there is also a microSD card slot, which supports up to 64GB microSD cards and this too is covered by a flip-out door. The top of the tablet is home to a lonely, 3.5mm audio output port, and the right spine houses the power key, the volume rocker and the IR blaster. The bottom end, has the micro-USB port and the stereo speakers.
The back of the device is punctuated by a Samsung logo in the middle, and the top left corner has the 5-megapixel camera. The camera does not get a flash companion so, it’s safe to say the low-light performance is nothing exceptional. Overall we also found that the colors depicted in the photos were not very accurate and looked a wee bit over-saturated.

Hardware:

 

Probably the biggest problem with the Galaxy Tab 3 311 is that unlike most Samsung products, it just does not resonate to the consumer in terms of its cutting edge specs.

What we get is a tablet that runs on a dual-core Exynos processor, which is clocked at 1.5GHz, 1.5GB of RAM, a Mali-400 GPU, 16GB of internal memory, a 4,450 mAh battery, a 5-megapixel rear camera, a 1.3-megapixel front facing camera, an 8-inch Super AMOLED display with a resolution of 1280×800 pixels. Additionally, it has the ability to make phone calls, something which neither the iPad mini nor the Nexus 7 can claim to do.
On a personal level, we are averse to the idea of using such a large device to make phone calls, but one is cognisant of the market dynamics and consumer needs and hence this indeed turns out to be a popular feature, especially for consumers in India.

Software:

 

One of the main reasons people revert to Samsung devices is that in the scheme of things, their products tend to have some of the newer versions of Android installed out of the box and lot of the software features are unique. Obviously, this is a double edged sword as the Galaxy S4 proved to be, but mostly people like these features due to the familiarity born out of the popularity of the brand and the convenience of Android. Though, again, we are not big fans of the cartoonish design ethos of Samsung’s TouchWiz user-interface.

Running on Android 4.2.2 Jelly Bean, the Galaxy Tab 3 311 runs on a totally ‘Samsunged’ version of Android which is loaded to the hilt with extra software features that are a part of the TouchWiz package. So features like Multi-Window multitasking are present, but it does not work perfectly which is most probably due to the underpowered nature of the device. Other software features include a Reading Mode which can be assigned to any app but works well with apps like Kindle or the web browser. There is also Samsung’s own Memo app, a smart remote app that is there to be used with the IR Blaster, S-Translate and Story Album.
The Smart Remote app recognises Samsung TVs, but configuring it with DTH services like Tata Sky requires a bit of imagination. It’s also not as feature rich as the solution provided by LG on its smartphones, which we deem to be vastly superior.
As always, Samsung has modified stock apps like the music player, the video player and the gallery. The gallery, for instance, gets deeply integrated with DropBox and all the images from DropBox get synced in the gallery app. Users also get the benefit of 50GB of free DropBox storage.
Overall, one is getting a pretty standard Samsung software package, which mostly works as advertized but can become a tad confusing to the layman just because of the sheer wealth of functionality.

Performance:

 

Right from the start it was pretty evident that the Galaxy Tab 3 311 was going to be no speed demon. That being said, the Galaxy Tab 3 311 performs perfectly fine for a tablet that one would use to consume media, browse the web and read books on. It delivers solid battery life and can last for around 8 hours of usage on a single charge with 3G enabled on the SIM card.

Of course, as it is powered by an older generation the 1.5GHz Exynos dual-core chip, its performance is not in the same league as the Galaxy S4 smartphone. However, navigation of the user interface remains smooth for the part and there are no major glitches in the navigation of the UI. In terms of gaming it falls behind the iPad mini and the Nexus 7, which basically have more powerful GPU stacks, so games like Dead Trigger just don’t feel as graphically realistic as one would experience it on the aforementioned tablets.
For reading and watching videos, the Galaxy Tab 3 311 is a brilliant tablet thanks to its sublime Super AMOLED panel which offers insanely deep blacks, good viewing angles, and decent outdoors legibility. People who find the colors of the Super AMOLED panel to be overly saturated can manually adjust the color temperature through a setting Samsung has provided. The user gets a number of options in this regard including an Adobe RGB setting. The reading mode in particular reduces the stress on the users eye while he/she is reading a book for long periods.


The 5-megapixel shooter on the back reproduced perfectly decent images in normal lightning, but the moment one took it in a dimly lit environment, the lack of the flash became evident and the images were pretty abysmal. Anyways we are not big proponents of clicking pictures with a tablet, so this should not be a deal breaker for most.
The call quality on the tablet was decent. We faced issues regarding volume levels and sometimes the caller on the other-end would fail to hear us as the microphone was so far away. This is a relatively common problem with tablet/phone hybrids and this issue can be daily mitigated by using an earphone with inline mic.

Verdict:

 

he Galaxy Tab 3 311 is a perfect Android tablet for someone who is looking for sub-10-inch tablet with calling as it provides an excellent ergonomic design, a great screen, solid battery life and calling facility in one package. At Rs 25,500 it also is a little expensive, and if one does not want the calling functionality, then Google’s Nexus 7 definitely comes out on top, though there are certain advantages the Galaxy Tab 3 311 provides over the Nexus 7 which include a rear camera, a lighter and more ergonomic design, a better screen and a microSD card slot that supports 64GB of storage.


 

 


 


 

 

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Grand Theft Auto V: Review:


There are good games, there are great games and then there is Grand Theft Auto. For more than a decade, Rockstar’s action-adventure has set a high standard for open world games and then raised them with each new iteration. With GTA V, all those benchmarks have been obliterated and the game has been pushed to unimaginable heights. I got to spend a considerable time playing and exploring every possible aspect of the game and here are my two cents on it.

GTA V is based in San Andreas and you spend most of the time in and around the city of Los Santos. With a map that is more than twice the size of Liberty City in GTA IV, there is a lot to do besides the usual driving around shooting people. San Andreas is a living and breathing world with people going about living their lives without bothering about what you do. You can see girls in bikinis walking their dogs at Vespucci beach, a couple of drunken rednecks fighting outside a bar or gangbangers doing a drive-by at Grove Street. If you were to stand and stare at your surroundings, you could see so much going on around you. This gives you an immense sense of freedom as you go about exploring a world where anything can happen.
From the very first moment you lay your eyes on the game, you sense that everything has been tweaked and improved from GTA IV. The world is grander and looks absolutely gorgeous, the character animations have been considerably improved, the combat system feels a little less irritating and the cars feel more like cars rather than hovercraft gliding on roads.


The level of detail is so insane, it feels as if Rockstar has put each aspect of the game under the microscope and tweaked and re-tweaked them until they were perfect. The combat system, which seems to have taken the best bits out of Max Payne and Red Dead Redemption, feels much improved and reliable. As I mentioned above, the automobiles too have been greatly improved and they feel more plied to the roads. Cars have their unique way of handling based on their class, so a sedan won’t drive like a tank or an SUV. That said I did feel that the steering could have been a little less sensitive and wish that flying the helicopters was less pain in the a**.
All these improvements mean that our ageing consoles have to strain to run everything smoothly and it’s no surprise they stutter in between. In some of the busier parts of the game or when I played for long periods, I noticed the occasional drop in framerate and some rare texture pop-ins. But they are few and far between and don’t warrant more than a grunt of frustration.
Moving on to the story and narration; Rockstar has moved on from the single protagonist to three wildly different protagonists. The story revolves around Michael De Santa, Franklin and Trevor Phillips in a post-economic crisis America where the ‘American Dream’ is a part of history textbooks. All the three characters hailing from different parts of the city have their own story and special abilities.

 Michael is a retired con artist going through a mid-life crisis, who besides lazing around his pool with a drink in his hand, loves complaining about his family and their expensive therapist. Franklin hails from the poorer parts of Los Santos, trying to escape the life of a gangbanger, but can’t quite escape the temptations of a bigger score. Trevor, though is the most volatile and dynamic character in the game— a psychotic murdering redneck high on methamphetamine and bordering on insanity. These characters also have their own special abilities, which help a lot during missions— Michael can go into Bullet Time ala Max Payne during a gunfight, Franklin can slow down time to make some impossible maneuvers while driving a car, and Trevor’s temporary Kratos-like rage mode helps him deal more damage and take less in return.
When not on a mission, you can freely switch between the three and continue what they had been doing. But Rockstar has hit the bull’s-eye when it comes to using the three characters together in a mission. Many of them are too big to be done by a single character and more often than not they will take each other’s help. Thankfully the characters also have their own set of missions, which balances the pace of the main storyline quite well. This is a welcome change from the earlier games, where you had only one character to live with and forced to relate to.
Coming to the missions themselves, each of them have been crafted to perfection and blown up to larger-than-life proportions. Almost every main mission needs the characters to get together, meticulously plan on if to go stealthily or go all guns blazing. The scale of the missions can be compared to some of Michael Bay’s over-the-top films. To give you an example, one of the mission has Trevor flying a plane into a larger cargo plane, taking out the soldiers, hijacking it and then jumping out of it to see it crash into the sea below. Another mission has Franklin dressed up as James Bond and stealing an Aston Martin DB5 look-a-like with the mini guns, spikes and the famous ejector seat.


There are many such memorable moments, but I rather not spoil them for you. One of the most welcome changes is the checkpoint system, which saves you a whole lot of trouble of driving back to the destination in case you fail the mission. Now you can restart from the said checkpoints every time you fail the mission, and in case you fail more than three times, the game also gives you the option of skipping the mission all together. Though purists might cringe over this, for the not-so-professional gamers this could prove a boon.
There are also a lot of other things you can do in the game like play tennis, golf, go to strip clubs or trade in stock market. Every character also comes across some ‘freaks or strangers’ who are poor souls of Los Santos asking for help. Do not miss out on those missions!
On top of everything, GTA V is also an immensely intelligent and witty game. It’s a full blown satire and the game’s writers have been given all the freedom to target everybody from celebrities, the government to the common man. Apart from fake soap operas on TVs or billboards across the state, it’s the radio that is the wittiest. From ads selling the American Dream to the breaking news about a guy who died standing in line for the latest ‘iFruit’ phone, they are all very well written. Then there’s the smartphone which along with providing a way to contact people, and read emails also lets you access ‘Life Invader’, a spoof of Facebook. Talking of radio, the in-game music is top-notch with a huge collection of licensed music catering to all kinds of tastes. If songs are not what you want in the game, then the background score during the heist missions really reflects the atmosphere well.
Rockstar has also seen to it that you don’t get withdrawal symptoms when you are away from your TV living your actual life. With the iFruit app on your iOS devices, you can buy new cars or planes and modify them at LS Customs. The best part is when you power up the game the next time, your new customized car will be waiting for you at the garage.

Verdict:

 

As you might have guessed from my 1,000-odd word rambling that GTA V  is one of, if not THE best game you could buy today. Rockstar has taken the best bits from all its earlier games, including the previous GTA iterations, and mixed them into a heady concoction. It is the one game you need to experience and a game that will easily satisfy you for the next six months or so. With the multiplayer world opening later today, just image how awesome it would be to roam around this fantasy world with your friends.
GTA V is available for Sony’s PlayStation 3 and Microsoft’s Xbox 360 for Rs 2,999.

 



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