Answer: Limits of composite functions Evaluate the

Chapter 9, Problem 63AE

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QUESTION:

Limits of composite functions  Evaluate the following limits.

\(\lim _{(x, y) \rightarrow(1,0)} \frac{\sin x y}{x y}\)

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QUESTION:

Limits of composite functions  Evaluate the following limits.

\(\lim _{(x, y) \rightarrow(1,0)} \frac{\sin x y}{x y}\)

ANSWER:

Step 1 of 4

Now in this case the function is not continuous at the point in question and so we can’t just plug in the point.                                                          

Since the  is not continuous at a point there is at least chance that the limit doesn’t exist.

Two of the more common paths to check are x and y-oxis.

 

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