find limit of h->0 [f(8+h)-f(8)]/(h) where f(x)=sqrt(x)-8

Answer 1

f(8+h) = sqrt (8+h) - 8
f(8) = sqrt(8) - 8
subtract
sqrt (8+h) -sqrt (8)
but
d/dh (8+h)^.5 = .5 (8+h)^-.5
so
sqrt (8+h) = sqrt 8 + .5 h/sqrt(8+h)
subtract sqrt 8
.5 h/sqrt(8+h)
divide by h
.5/sqrt (8+h)
let h -->0
.5/sqrt 8