Need help urgently, thank you! Consider the following limit.lim(x. )- (0, 0) x + 3y4a) Evaluate limit along the path y-3x.9.limK-(0, 0) x + 3y4244b) Does the limit exist? If so, find its value. If not, answer DNE. In either case, Use the Show My Work space to explain using specificmathematical reasoning.lim(x. )- (0, 0) x + 3y4x DNEShow Mu

Name: Need help urgently, thank you! Consider the following limit.lim(x. )-
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Description: Need help urgently, thank you! Consider the following limit.lim(x. )- (0, 0) x + 3y4a) Evaluate limit along the path y-3x.9.limK-(0, 0) x + 3y4244b) Does the limit exist? If so, find its value. If not, answer DNE. In either case, Use the Show My Work

the given limit is limx,y→0,0x2y2x4+3y4 to evaluate the limit along y=-3x…

Answered: following limit. lim (x.)- (0, 0) x +…

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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Need help urgently, thank you!

Consider the following limit.
lim
(x. )- (0, 0) x + 3y4
a) Evaluate limit along the path y-3x.
9.
lim
K-(0, 0) x + 3y4
244
b) Does the limit exist? If so, find its value. If not, answer DNE. In either case, Use the Show My Work space to explain using specific
mathematical reasoning.
lim
(x. )- (0, 0) x + 3y4
x DNE
Show Mu

Expert Solution

Step 1

the given limit is $l i m_{(x, y) \to (0, 0)} \frac{x^{2} y^{2}}{x^{4} + 3 y^{4}}$

to evaluate the limit along $y = - 3 x$

$\begin{array}{rcl} l i m_{(x, y) \to (0, 0)} \frac{x^{2} y^{2}}{x^{4} + 3 y^{4}} & = & l i m_{x \to 0} \frac{x^{2} {(- 3 x)}^{2}}{x^{4} + 3 {(- 3 x)}^{4}} \\ = & l i m_{x \to 0} \frac{x^{2} (9 x^{2})}{x^{4} + 3 (81 x^{4})} \\ = & l i m_{x \to 0} \frac{9 x^{4}}{x^{4} + 243 x^{4}} \\ = & l i m_{x \to 0} \frac{9 x^{4}}{x^{4} (1 + 243)} \\ = & l i m_{x \to 0} \frac{9 x^{4}}{x^{4} (244)} \\ = & \frac{9}{244} \end{array}$

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