Question

hi, how do u solve this problem using limit notation. I tried it but go stuck at the last part.
find f'(x) for f(x)=Sqrt2x-1
using F(x+h)-f(a)/h

i got to the end and i got 1/Sqrt2x-1 -sqrt2x-1. i don't know wht u do next? am i right so far?

Answer 1

f'= f(x+h)-f(x) / h as h >>0
= sqrt(2x+2h-1) - sqrt(2x-1) /h
multiply numerator by the conjugate...

= (2x+2h-1)-(2x-1) )/h(sqrt(2x+2h-1)+sqrt(2x-1) )
= 2h/(h(sqrt(2x+2h-1)+sqrt(2x-1) )
= 2/(2sqrt(2x-1)= 1/sqrt(2x-1)

check my thinking.