at-what-points-x-y-z-in-space-are-the-functions-in-exercises-31-34-continuous-beginarrayltext-a-fx-y

Question

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

Uma Kumari · Accepted 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.

Uma Kumari · 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.

Stephen Hobbs · Answer

for the first function the natural log we want to ensure, uh, well, First off, we could say that this is going to be continuous for all real numbers X, y and Z. With a few restrictions, we know that the product for a natural log inside the argument must be greater than zero. And then furthermore, um, none of these can equal zero. And so we could also just say X cannot equal zero. Why cannot equal zero z canonical zero and these are the main restrictions here for Part B. We just need to ensure that well, actually, he to anything is going to be continuous on co sign for any argument is also going to be continuous. So really the exponential and continuous or both, and co sign for both continuous for all values X y and

Stephen Hobbs · Answer

the first function will be continuous everywhere because it is just the Siris of polynomial, and so it&#x27;ll be continuous for all X y and Z values. And the second part, we know that discontinuities would exist for anything negative under the square root. And so we could say all X, Y and Z values. With the restriction that expired, what&#x27;s Y squared must be greater than or equal to one. So we could just add one to both sides there, and then that would satisfy that second condition there.

Problem

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

Problem 32 Easy Difficulty

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

Answer

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

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

Thomas Calculus

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

Vectors Intro

Vector Basics - Example 1

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

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

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

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

Thomas Calculus