Question

Let\\ f(x,y) = \begin{cases} \frac{\sqrt{x} - \sqrt{y+2}}{x-y-2}, & \text{if } (x,y) \neq (4,2) \\ m, & \text{if } (x,y) = (4,2) \end{cases}\\For which value of the real number m the function f(x, y) is continuous at the point (4, 2)?\\Select one:\\a. 1\\b. \frac{1}{4}\\c. \frac{1}{2}\\d. \frac{1}{5}\\e. 0

          Let\\
f(x,y) = \begin{cases} \frac{\sqrt{x} - \sqrt{y+2}}{x-y-2}, & \text{if } (x,y) \neq (4,2) \\ m, & \text{if } (x,y) = (4,2) \end{cases}\\For which value of the real number m the function f(x, y) is continuous at the point (4, 2)?\\Select one:\\a. 1\\b. \frac{1}{4}\\c. \frac{1}{2}\\d. \frac{1}{5}\\e. 0

Let

f(x,y) = (√(x) - √(y+2))/(x-y-2), if (x,y) ≠(4,2)
m, if (x,y) = (4,2)
For which value of the real number m the function f(x, y) is continuous at the point (4, 2)?
Select one:
a. 1
b. (1)/(4)
c. (1)/(2)
d. (1)/(5)
e. 0

Added by Noelia -.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

04/21/2022

Step 1

Step 1: For the function to be continuous at $(4,2)$, the limit of $f(x,y)$ as $(x,y)$ approaches $(4,2)$ must exist and be equal to $f(4,2)$. Show more…

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Let $$f(x,y) = \begin{cases} \frac{\sqrt{x} - \sqrt{y + 2}}{x - y - 2}, \text{ if } (x,y) \neq (4,2) \\ m, \text{ if } (x,y) = (4,2) \end{cases}$$ For which value of the real number $m$ the function $f(x,y)$ is continuous at the point $(4,2)$? Select one: a. 1 b. $\frac{1}{4}$ c. $\frac{1}{2}$ d. $\frac{1}{5}$ e. 0