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Solved: Limits of composite functions Evaluate the
Chapter 9, Problem 66AE(choose chapter or problem)
QUESTION:
Limits of composite functions Evaluate the following limits.
\(\lim _{(x, y) \rightarrow(0, \pi / 2)} \frac{1-\cos x y}{4 x^{2} y^{3}}\)
Questions & Answers
QUESTION:
Limits of composite functions Evaluate the following limits.
\(\lim _{(x, y) \rightarrow(0, \pi / 2)} \frac{1-\cos x y}{4 x^{2} y^{3}}\)
ANSWER:Solution 66AE
Step 1 of 3:
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)).