Answer to Question #203417 in Calculus for Rajay Myrie

Question

Evaluate lim𝑥→2 𝑥 3−2𝑥 2+4𝑥−8 𝑥 4−2𝑥 3+𝑥−2

Answer 1

Let us evaluate the limit:

$\lim\limits_{𝑥\to 2}\frac{ 𝑥^3−2𝑥^2+4𝑥−8}{ 𝑥^4−2𝑥^3+𝑥−2}= \lim\limits_{𝑥\to 2}\frac{ (x-2)(𝑥^2+4)}{ (x-2)(𝑥^3+1)}= \lim\limits_{𝑥\to 2}\frac{ 𝑥^2+4}{𝑥^3+1}=\frac{ 2^2+4}{2^3+1}=\frac{8}{9}.$