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At what points $(x, y, z)$ in space are the functions in Exercises $31-34$ continuous?a. $h(x, y, z)=x y \sin \frac{1}{z} \quad$ b. $h(x, y, z)=\frac{1}{x^{2}+z^{2}-1}$

a) The function is continuous for all $(x, y, z) .$ However, all values of $z$ should not be zero.b) The function is continuous at each point $(x, y, z),$ however $x^{2}+z^{2} \neq 1$

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 to find at what point the given function is continues now. In part a were given function. H X y said is equals toe X y sign one over there. Now the function is continuous for all X y zed. Except the values off said should not be zero, that is, Zed should not equal toe zero now coming toe part B, we have the given function edge. X y zed is equals toe one over X square, plus that square minus one. Now the function is continuous at each point off X y zed, however X square plus that's where should not equal toe one. So there's the solution.

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