<s>[INST] What is $ \lim_{(x,y)\to(2,2)}\frac{x^4-y^4}{x^2 - y^2} $? I have limit:
$$
\lim_{(x,y)\to(2,2)}\frac{x^4-y^4}{x^2 - y^2}
$$
Why is the result $8$ ?
 [/INST] The limit you are looking up to has a 'hole' in its value as $(x,y)\rightarrow(2,2)$. In order to eradicate that, we have to factor out the hole which is quite easy in this case. It can be done as follows:
$$\lim_{(x,y)\rightarrow(2,2)}\dfrac{x^4-y^4}{x^2-y^2}=\lim_{(x,y)\rightarrow(2,2)}\dfrac{(x^2+y^2)(x^2-y^2)}{x^2-y^2}=\lim_{(x,y)\rightarrow(2,2)}x^2+y^2$$  
Now we have successfully removed the 'hole' in the value by getting rid of the $\dfrac00$ format of the expression.  
Now, substituting the values of $x$ and $y$ in the expression gives us,
$$\lim_{(x,y)\rightarrow(2,2)}x^2+y^2=2^2+2^2=4+4=8$$  
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