Evaluate the limit, if it exists. lim h?0 sqrt 25 + h - 5/h

Question

Please help me

Answer 1

Rationalize the numerator by multiplying  the numerator and denominator by the conjugate of the numerator:

 

(√(25+h) - 5)/h = [(√(25+h) - 5)/h][(√(25+h) + 5)/(√(25+h) + 5)]

 

                       = (25 + h - 25)/[h(√(25+h)+5)]

 

                       = h/[h(√(25+h)+5)]

 

                       = 1/[√(25+h)+5]

 

Taking the limit as h→0, we get 1/[√25 + 5] = 1/10