Limits of composite functions Evaluate the following

Chapter 9, Problem 65AE

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QUESTION:

Limits of composite functions  Evaluate the following limits.

\(\lim _{(x, y) \rightarrow(0,2)}(2 x y)^{x y}\)

Questions & Answers

QUESTION:

Limits of composite functions  Evaluate the following limits.

\(\lim _{(x, y) \rightarrow(0,2)}(2 x y)^{x y}\)

ANSWER:

Solution 65AE

Step 1 of  2:

In this problem we need to evaluate

We know that f(g(x,y)) is called as a composite function.

Consider ,    is  a composite function …………..(1)

Let us consider , g(x , y) = xy = t

Then    =  = f(t).

By finding the limit of  f( g(x , y)) , first find the g(x,y) then find the limit of f(g(x,y)).

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