Let f(x, y) = (Give exact answers. Use symbolic notation and fractions where needed.) f(x,-2x) = f(x, 3x) = 2x² + 3y Calculate f(x, mx) at m = -2 and m = 3. xy Calculate the following limits. (Give exact answers. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) (x,-2x) (0,0) lim f(x,-2x) = (x,y)→(0,0) lim f(x, 3x) = (x,3x) (0,0) lim f(x, y) = DNE
Let f(x, y) = (Give exact answers. Use symbolic notation and fractions where needed.) f(x,-2x) = f(x, 3x) = 2x² + 3y Calculate f(x, mx) at m = -2 and m = 3. xy Calculate the following limits. (Give exact answers. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) (x,-2x) (0,0) lim f(x,-2x) = (x,y)→(0,0) lim f(x, 3x) = (x,3x) (0,0) lim f(x, y) = DNE
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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Question
![Let \( f(x, y) = \frac{2x^2 + 3y^2}{xy} \). Calculate \( f(x, mx) \) at \( m = -2 \) and \( m = 3 \).
(Give exact answers. Use symbolic notation and fractions where needed.)
\[ f(x, -2x) = \]
\[ f(x, 3x) = \]
Calculate the following limits.
(Give exact answers. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.)
\[
\lim_{(x, -2x) \to (0,0)} f(x, -2x) =
\]
\[
\lim_{(x, 3x) \to (0,0)} f(x, 3x) =
\]
\[
\lim_{(x, y) \to (0,0)} f(x, y) = \text{DNE}
\]
There are no graphs or diagrams in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F646bd109-e2a6-4c6a-a3ea-1fdf7467c156%2Fbb23bcb6-be7b-461b-9b0f-88ee4a944d68%2Fp9eno4w_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( f(x, y) = \frac{2x^2 + 3y^2}{xy} \). Calculate \( f(x, mx) \) at \( m = -2 \) and \( m = 3 \).
(Give exact answers. Use symbolic notation and fractions where needed.)
\[ f(x, -2x) = \]
\[ f(x, 3x) = \]
Calculate the following limits.
(Give exact answers. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.)
\[
\lim_{(x, -2x) \to (0,0)} f(x, -2x) =
\]
\[
\lim_{(x, 3x) \to (0,0)} f(x, 3x) =
\]
\[
\lim_{(x, y) \to (0,0)} f(x, y) = \text{DNE}
\]
There are no graphs or diagrams in the image.
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