How do you solve this?

Question

Use L'Hospital's Rule:

Limit as x approaches 0, ((√5x+25)-5)/x

Answer 1

Straight substitution x=0 gives 0/0 so you can use the designated rule.

 

differentiate the numerator SEPARATELY and differentiate the denominator separately, and take the limit of those expressions as x approaches 0.

 

numerator will be ½(5x+25)^-½(5) and denominator will be 1.  when you take limit as x →0, you get ½ as final answer.