October 1st, 2018, 06:54 PM  #1 
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6  Multivariable Limits
Has anybody idea on what techniques I can apply on these limits? at c and d I did direct substitution since there is no zero at the denominator. Is that correct? a) I converted polar form and denominator became cos^2Theta+Sin^2theta = 1 so that limit exists how about b? no techniques I know work and I couldn't prove it DNE either. 
October 1st, 2018, 07:49 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340 
a) $\dfrac{x^4y^4}{x^2+y^2} = \dfrac{(x^2y^2)(x^2+y^2)}{x^2+y^2}=x^2y^2$ Now just plug the values in. b) $\lim \limits_{x\to 1\\y\to 1}~~\dfrac{xy}{x+y}$ at the limit values the numerator is finite and the denominator is 0 which suggest the limit is infinity. But by changing the direction you approach the limit point you can make the result head to either plus or minus infinity and thus the limit doesn't exist. c) $\lim \limits_{x\to 1 \\y \to 1}~~\dfrac{x^2 ye^y}{x^4+4y^2}$ just plug the values in. d) Same here, just plug the limit values in. I don't see why this problem would be harder. The graph looks perfectly smooth. 

Tags 
limits, multivariable 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
multivariable limit  Leonardox  Calculus  1  September 29th, 2018 11:51 PM 
Multivariable (maybe) Calculus Help  akansel  Calculus  6  October 16th, 2017 08:44 AM 
multivariable limit  SenatorArmstrong  Calculus  4  July 3rd, 2017 02:02 AM 
Multivariable Calculus  Ecomat  Math Books  1  July 2nd, 2012 03:07 AM 
Some Multivariable Questions  icecue7  Calculus  1  November 13th, 2007 03:54 PM 