Question

Im h--> 0

((Sqrt 9+h)-3)/h

Answer 1

`\lim_(h \to 0) ( √(9+h)-3)/(h) = ( √(9+0) -3)/(0)= (0)/(0) \\ \lim_(h \to 0) ( √(9+h)-3)/(h)* ( √(9+h)+3 )/( √(9+h) +3)= \\ = \lim_(h \to 0) (9+h-9)/(h( √(9+h) +3)) = \\ \lim_(n \to 0) (h)/(h( √(9+h)+3) )= \\ = (1)/( √(9) +3)`=
= 1/6