Question

Evaluate the limit using the appropriate limit law(s). (if an answer does not exist, enter dne.) lim x → 1 2x2 + 4 x2 + 4x − 4

Answer 1

Presumably, the limit to be evaluated is

$\displaystyle\lim_{x\to1}\frac{2x^2+4}{x^2+4x-4}$

Since the given function is continuous at $x=1$, the limit of function is equal to the value of the function at $x=1$:

$\displaystyle\lim_{x\to1}\underbrace{\frac{2x^2+4}{x^2+4x-4}}_{f(x)}=f(1)=\frac{2+4}{1+4-4}=6$