Answer:
[tex]\lim_{x\rightarrow 6}\frac{x^2-10x+24}{x-6}=2[/tex]
Step-by-step explanation:
We are given that
[tex]\lim_{x\rightarrow 6}\frac{x^2-10x+24}{x-6}[/tex]
We have to find the limit if exist.
Using factorization method factorize the numerator of given function.
[tex]\lim_{x\rightarrow 6}\frac{x^2-6x-4x+24}{x-6}[/tex]
[tex]\lim_{x\rightarrow 6}\frac{x(x-6)-4(x-6)}{x-6}[/tex]
[tex]\lim_{x\rightarrow 6}\frac{(x-6)(x-4)}{x-6}[/tex]
After cancel out the same factor of numerator and denominator we get
[tex]\lim_{x\rightarrow 6}(x- 4)[/tex]
[tex]6-4=2[/tex]
Hence, [tex]\lim_{x\rightarrow 6}\frac{x^2-10x+24}{x-6}=2[/tex]
