Limit of a Function of two variables

Limit of a two variable Function|IIT JAM 2016 |Problem 6

Find the value of $\lim\limits_{(x,y) \to (2,-2)} \frac{\sqrt{x-y}-2}{x-y-4}$ is

$0$
$\frac14$
$\frac13$
$\frac12$

Key Concepts

Function of Several Variables

Limit of a function of several variables

Check the Answer

Answer: $\textbf{(B)} \frac14$

IIT JAM 2016 (Problem 6)

Function of several variables: Fleming, Wendell H

Try with Hints

So, this problem has double limit. But we will not consider this first i.e., first try to solve the above limit without seeing $(x,y) \to (2,-2)$ , just like we used to do in our school days!!!

Here also we cannot put $x,y$ directly, as it will become undefined.

Now,

$\lim\limits_{(x,y) \to (2,-2)} \frac{(x-y)-4}{(x-y-4)(\sqrt{x-y}+2)}$ [Multiplied by $\sqrt{x-y}+2$ on numerator and denominator ]

Now again, try to simplify the above limit !!!

After simplifying,

We have,

$\lim\limits_{(x,y) \to (2,-2)} \frac{1}{\sqrt{x-y}+2}$ [ Since $(x,y) \to (2,-2) \Rightarrow x-y-4 \ne 0$ ]

Now in this part we will use the limits, i.e., $(x,y) \to (2,-2)$

$\Rightarrow \frac{1}{\sqrt{2+2}+2}=\frac14$ [ANS]

Other useful links

Limit of a two variable Function|IIT JAM 2016 |Problem 6

Find the value of $\lim\limits_{(x,y) \to (2,-2)} \frac{\sqrt{x-y}-2}{x-y-4}$ is

$0$
$\frac14$
$\frac13$
$\frac12$

Key Concepts

Function of Several Variables

Limit of a function of several variables

Check the Answer

Answer: $\textbf{(B)} \frac14$

IIT JAM 2016 (Problem 6)

Function of several variables: Fleming, Wendell H

Try with Hints

So, this problem has double limit. But we will not consider this first i.e., first try to solve the above limit without seeing $(x,y) \to (2,-2)$ , just like we used to do in our school days!!!

Here also we cannot put $x,y$ directly, as it will become undefined.

Now,

$\lim\limits_{(x,y) \to (2,-2)} \frac{(x-y)-4}{(x-y-4)(\sqrt{x-y}+2)}$ [Multiplied by $\sqrt{x-y}+2$ on numerator and denominator ]

Now again, try to simplify the above limit !!!

After simplifying,

We have,

$\lim\limits_{(x,y) \to (2,-2)} \frac{1}{\sqrt{x-y}+2}$ [ Since $(x,y) \to (2,-2) \Rightarrow x-y-4 \ne 0$ ]

Now in this part we will use the limits, i.e., $(x,y) \to (2,-2)$

$\Rightarrow \frac{1}{\sqrt{2+2}+2}=\frac14$ [ANS]

Other useful links

Leave a Reply Cancel reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

HALL OF FAME BLOG OFFLINE CLASS

CHEENTA ON DEMAND BOSE OLYMPIAD

Cheenta Academy Private Limited |

support@cheenta.com

Menu