Let † : R² → R be the function x2 if (x, y) + (0,0) f (x, y) = x + Y if (x, y) (0,0) By using the definitions only (as limits), compute both f-(0,0) and fy(0,0).
Let † : R² → R be the function x2 if (x, y) + (0,0) f (x, y) = x + Y if (x, y) (0,0) By using the definitions only (as limits), compute both f-(0,0) and fy(0,0).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let \( f : \mathbb{R}^2 \to \mathbb{R} \) be the function
\[
f(x, y) =
\begin{cases}
\frac{x^2}{x+y} & \text{if } (x, y) \neq (0, 0) \\
0 & \text{if } (x, y) = (0, 0)
\end{cases}
\]
By using the definitions only (as limits), compute both \( f_x(0, 0) \) and \( f_y(0, 0) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcaa0f822-544e-4e71-bb85-904850361648%2F8c1e65b2-0a9e-4be3-b28a-3952ecfd0f12%2Fn6b0qba_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( f : \mathbb{R}^2 \to \mathbb{R} \) be the function
\[
f(x, y) =
\begin{cases}
\frac{x^2}{x+y} & \text{if } (x, y) \neq (0, 0) \\
0 & \text{if } (x, y) = (0, 0)
\end{cases}
\]
By using the definitions only (as limits), compute both \( f_x(0, 0) \) and \( f_y(0, 0) \).
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