Question

Evaluate $\underset{x\to 5}{lim}\frac{x^3-5^3}{x^{}-5^{}}$.

Answer 1

Let $L=\underset{x\to 5}{lim}\frac{x^3-5^3}{x^{}-5^{}}$

The expression takes the form $\frac{0}{0}.$

Using L hospitals Rule,

$L=\underset{x\to 5}{lim}\frac{3x^2}{1}=3(5{)}^2=75$.