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Use the Squeeze Theorem to evaluate the limit \lim_{(x,y) \rightarrow (3,2)} (x^2-9)...

Question:

Use the Squeeze Theorem to evaluate the limit {eq}\lim_{(x,y) \rightarrow (3,2)} (x^2-9) \cos(\frac{1}{(x-3)^2+ (y-2)^2}) {/eq}

Squeeze Theorem

This theorem allows us to determine the limit of a function, once we delimit the expression of said functions between two other functions.

If the limit of both expressions are the same, we can assure that the limit of the function is equal to the limit of these two other functions.

Answer and Explanation:

Taking into account that:

{eq}- 1 \le \cos \left( {\frac{1}{{{{(x - 3)}^2} + {{(y - 2)}^2}}}} \right) \le 1 {/eq}

The expression of the limit can...

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Squeeze Theorem: Definition and Examples

from Math 104: Calculus

Chapter 6 / Lesson 6
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