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)(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{(2x^2+4)/(x^2+4x-4)}_(f(x))=f(1)=(2+4)/(1+4-4)=6`