at-what-points-x-y-z-in-space-are-the-functions-in-exercises-31-34-continuous-a-hx-y-zx-y-sin-frac1z

Question

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. $h(x, y, z)=\frac{1}{x^{2}+z^{2}-1}$

Uma Kumari · Accepted Answer

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&#x27;s where should not equal toe one. So there&#x27;s the solution.

Uma Kumari · Answer

in this problem we have to find at what point given function is continues now. In part eight, we have the given function edge. X y zed is equals toe one over moored off wife less more observed. The given function is continuous for all. Exercise that point except at X 00 now coming toe fight be we have the function f X y z is equals toe one over model ex wife plus model say now here Also, the function is continuous at at each point off X y zed, except zero by zero or X 00 So that&#x27;s a solution.

Uma Kumari · Answer

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.

Uma Kumari · Answer

in this problem. In the part a were given the polling function. F x y Z is equals two x squared plus y squared minus two. That&#x27;s where now the objective is to find the point x y Z in with the function f s continuous. Now there are no radicals, logarithms and fractions for the function f. So the function f is containing us for all point. That is X, y and Z. They now coming to part B. There is f x y zed is equals toe under rule X squared plus y squared minus one. Now her objective is to find exercise there, in which the function F is continuous. How the objective is to find the points exercise that is the function F is continuous. The square root function that is under X squared plus y squared minus one exists if X squared plus vice square minus one is greater than equal to zero or X squared. Plus y square is greater than equal to one. Therefore, the certain point where the function F is continuous is X y zed X squared plus y square is greater than equal to one that is the set off all points X Y Z except the interior off the surrender X squared plus y squared is equal to one, so that&#x27;s the solution.

Stephen Hobbs · Answer

or the function and part A we are looking for when it&#x27;s continuous, and in this case it&#x27;s going to be for all values, X and y. And then the only restriction on Z is that it cannot equal zero sense. It&#x27;s there would be a dividing by zero error. So, really, it&#x27;s all values. X y z. We cannot equal Syria. And for Part B, we just need to ensure again that there&#x27;s not dividing by zero error or undefined portion. And so again we could go ahead and say all real values. X y Z. In this case, we wanna set up that expert plus Z squared minus one does not equal zero or adding one to both sides. X squared plus Z squared does not equal one is the same, and that&#x27;s it.

Stephen Hobbs · Answer

because the natural log is only defined for positive values. Will say that the domain, for part, is all real values. X, y and Z with the restriction that Z minus sex word minus y squared minus one must be greater than zero. But we could just go ahead and add that one to both sides, and another way to state that is the minus. Export minus y squared must be greater than one for Part B. We have an issue with dividing by zero error, and the domain year will include all real values X, Y and Z, with the condition that Z minus square root of X squared plus y squared can not equal zero. But another way to state that is just to add the negative term over and so really would just become a positive X squared. What&#x27;s why it&#x27;s weird. Does not people see so really always? Did it set the denominator equal zero and then moved to the negative turn over

Problem

At what points $(x, y, z)$ in space are the funct…

Problem 33 Easy Difficulty

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. $h(x, y, z)=\frac{1}{x^{2}+z^{2}-1}$

Answer

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 $x^{2}+z^{2} \neq 1$

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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 $x^{2}+z^{2} \neq 1$

Thomas Calculus

Lily A.

Catherine R.

Caleb E.

Samuel H.

Vectors Intro

Vector Basics - Example 1

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. GiordanoThomas Calculus

Lily A.

Catherine R.

Caleb E.

Samuel H.

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 $x^{2}+z^{2} \neq 1$

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano

Thomas Calculus