Question

The value of $\underset{x\to 5}{\lim }\frac{x^3-125}{x^2-7x+10}$ is

Answer 1

$\underset{x\to 5}{\lim }\frac{x^3-125}{x^2-7x+10}=\underset{x\to 5}{\lim }\frac{\left(x-5\right)\left(x^2+5x+25\right)}{x^2-5x-2x+10}=\underset{x\to 5}{\lim }\frac{\left(x-5\right)\left(x^2+5x+25\right)}{\left(x-5\right)\left(x-2\right)}=\underset{x\to 5}{\lim }\frac{\left(}{x^2+5x+25}=\frac{75}{3}=25$