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The Sandwich Theorem for functions of two variables states that if $g(x, y) \leq f(x, y) \leq h(x, y)$ for all $(x, y) \neq\left(x_{0}, y_{0}\right)$ in a disk centered at $\left(x_{0}, y_{0}\right)$ and if $g$ and $h$ have the same finite limit $L$ as $(x, y) \rightarrow\left(x_{0}, y_{0}\right),$ then$$\lim _{(x, y) \rightarrow\left(x_{0}, y_{0}\right)} f(x, y)=L$$Use this result to support your answers to the questions in Exercises $45-48 .$Does knowing that $|\cos (1 / y)| \leq 1$ tell you anything about$$\lim _{(x, y) \rightarrow(0,0)} x \cos \frac{1}{y} ?$$Give reasons for your answer.

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Calculus 3

Calculus 1 / AB

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Applications of the Derivative

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it is given that co signed into one upon by mode smaller than equals to one we need to find limit. It's common by tends to zero comma zero extent to co sign into one upon by the limit is zero sense Cosigned man upon by mold is smaller than equals to one. We know that a science data lies between minus one and one, so we begin minus one is smaller than equals To consign integon upon by which is smaller than equals toe one might apply the whole function by AEG speak it minus X, which is smaller than equals toe eggs into designing toe one upon by which is smaller than equals two way four x s greater than equals to zero For access Mulligan equals to zero minus X is greater than equals two weeks into co sign into one upon by which is greater than equal straight. So we take the limits off minus X and Eggs LTD's comma via tends to zero comma zero minus x toe get zero and lim X coma via tends to zero comma zero. Okay, get zero by the sandwich there, um, we get g o h comma by a smaller than equals to a perfect storm of I, which is also smaller than equals to a topics comma. Then Lim X comma vitamins to zero comma zero is extent to co sign into one upon by also tends to zero. Does the required solution is zero. This is done so

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