September 29th, 2018, 10:33 PM  #1 
Senior Member Joined: Apr 2017 From: New York Posts: 119 Thanks: 6  multivariable limit
in this limit: should I go this way (1) plug in x=1 and simplify the equation and (2) plug y=1 and simplify the equation or there is some more advanced method that I should apply and I can't see? 
September 30th, 2018, 12:51 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,316 Thanks: 1230 
multivariable limits are tricky. The possible limits all need to exist and agree when being evaluated in any direction in order for the limit to actually exist. Generally when you see problems like this some factoring or similar will remove the 0 from the denominator if it exists. In this problem just plug the values in $\dfrac{2(1^2) + 3(1)(1) + 4((1)^2)}{3(1^2)+5((1)^2)} = \\ \dfrac{23+4}{3+5}=\dfrac{3}{8}$ 

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limit, multivariable 
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