Question

Lim (h->0) (sqrt(25+h)-5)/h.

Answer 1

`\lim_(h \to 0) ( √(25+h) -5)/(h)= (0)/(0)`
We have to multiply numerator and denominator by: √(25-h)+ 5:

`\lim_(h \to 0) ( √(25+h)-5)/(h)* ( √(25+h) +5)/( √(25+h)+5) = \\ \lim_(h \to 0) (25+h-25)/(h( √(25+h)+5) ) = \\ \lim_(h \to 0) (1)/( √(25+h) +5) = \\ = (1)/(5+5)=`= 1/10 = 0.1