1. Verify that the following limits do not exist by finding two different paths approaching the point (0, 0) that give different values for the limit. [3 each] a. 2 x² - y² lim (x,y) (0,0) x² + y² 3. Assuming that the equation below defines quids (you can class x²y b. lim ' (x,y) →(0,0) x4 + y 2 way like) [4]
1. Verify that the following limits do not exist by finding two different paths approaching the point (0, 0) that give different values for the limit. [3 each] a. 2 x² - y² lim (x,y) (0,0) x² + y² 3. Assuming that the equation below defines quids (you can class x²y b. lim ' (x,y) →(0,0) x4 + y 2 way like) [4]
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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![**1. Verify that the following limits do not exist by finding two different paths approaching the point (0, 0) that give different values for the limit. [3 each]**
a. \(\lim_{{(x, y) \to (0, 0)}} \frac{x^4 - y^2}{x^2 + y^2}\)
b. \(\lim_{{(x, y) \to (0, 0)}} \frac{x^2 y}{x + y^2}\)
2. Assuming that in equation below defines y as a differentiable function of x, find dy/dx. (You can use the easy way we did in class, or another way if you’d like) (3).
\(x^3 y + y^2 - 3x - 7y + f(y(x)) = 5\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14851614-7f15-4b21-be9e-fda332bc9b7d%2Fda3a5a79-e966-4687-b35c-8e4179c97e52%2Fnp6pe8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**1. Verify that the following limits do not exist by finding two different paths approaching the point (0, 0) that give different values for the limit. [3 each]**
a. \(\lim_{{(x, y) \to (0, 0)}} \frac{x^4 - y^2}{x^2 + y^2}\)
b. \(\lim_{{(x, y) \to (0, 0)}} \frac{x^2 y}{x + y^2}\)
2. Assuming that in equation below defines y as a differentiable function of x, find dy/dx. (You can use the easy way we did in class, or another way if you’d like) (3).
\(x^3 y + y^2 - 3x - 7y + f(y(x)) = 5\)
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