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September 29th, 2018, 09:33 PM   #1
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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?
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September 29th, 2018, 11:51 PM   #2
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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{2-3+4}{3+5}=\dfrac{3}{8}$
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