Question

if f(x)=sqrt(x) find and simplify (f(a+h)-f(a))/h where h cnt=0

Answer 1

[sqrt(a+h) - sqrt(a)] / h = [(sqrt(a+h) - sqrt(a)) * (sqrt(a+h) + sqrt(a))] / [h*(sqrt(a+h) + sqrt(a))] = (a+h-a) / [h*(sqrt(a+h) + sqrt(a))] = 1 / (sqrt(a+h) + sqrt(a))
take the limit now
1/(2sqrt(a))
which is the derivative of sqrt(x) at x=a.

Answer 2

i just multiplied by a form of 1 : (sqrt(a+h) + sqrt(a))/(sqrt(a+h) + sqrt(a))

Answer 3

ok makes sense, been awhile since iv done them and cant find it in the book so thanks for the reminder