Question

Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x → 6 (x2 − 10x + 24)/ (x − 6)

Answer 1

Answer:

$\lim_{x\rightarrow 6}\frac{x^2-10x+24}{x-6}=2$

Step-by-step explanation:

We are given that

$\lim_{x\rightarrow 6}\frac{x^2-10x+24}{x-6}$

We have to find the limit if exist.

Using factorization method factorize the numerator of given function.

$\lim_{x\rightarrow 6}\frac{x^2-6x-4x+24}{x-6}$

$\lim_{x\rightarrow 6}\frac{x(x-6)-4(x-6)}{x-6}$

$\lim_{x\rightarrow 6}\frac{(x-6)(x-4)}{x-6}$

After cancel out the same factor of numerator and denominator we get

$\lim_{x\rightarrow 6}(x- 4)$

$6-4=2$

Hence, $\lim_{x\rightarrow 6}\frac{x^2-10x+24}{x-6}=2$