Question

Solve: limx→ 4 (x² - 5x + 4)/(x² –2x − 8)

Answer 1

Given:

The limit

`\lim_(x\to4)((x^2-5x+4)/(x^2-2x-8))`

Required:

Solve limit.

Explanation;

We have

`\begin{gathered} \lim_(x\to4)((x^2-5x+4)/(x^2-2x-8)) \\ \text{ If apply limit now we will get }(0)/(0)\text{ form} \\ So,\text{ we will apply L'hopital rule} \\ \lim_(x\to4)((2x-5)/(2x-2)) \\ =(8-5)/(8-2) \\ =(3)/(6) \\ =(1)/(2) \end{gathered}`

Answer:

`\text{ Limits is }(1)/(2).`