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At what points $(x, y, z)$ in space are the functions in Exercises $31-34$ continuous?$$\begin{array}{l}{\text { a. } f(x, y, z)=x^{2}+y^{2}-2 z^{2}} \\ {\text { b. } f(x, y, z)=\sqrt{x^{2}+y^{2}-1}}\end{array}$$

a) $x y z>0$b) The function is continuous at each point of $(x, y, z)$

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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in this problem, we have toe find at what point the function is continuous and in part a We are given function. F x y Z is equal school Ln x wise, they or the function is continuous for X y z. However, all x y zed, the points should be greater than zero. Therefore, X y zed greater than zero Now coming toe pipe b, we are given function. X y zed is equals toe Ito the Power X plus y for science there Now the function is a continuous at each point off X y and then so there is a solution.

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