Consider the function f : R2 → R defined byf (x, y) =cos x sin yy if y̸ = 0cos x if y = 0.Is f continuous everywhere? Justify your answer
Question
Solution 1
The function f(x, y) is continuous everywhere. Here's why:
The function f(x, y) is defined as cos(x)sin(y)/y for y ≠ 0 and cos(x) for y = 0.
For y ≠ 0, the function cos(x)sin(y)/y is a composition of continuous functions, hence it is continuous.
For y = 0, the function is simply cos(x), Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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