f(x+h) = 1/(2x+2h)
f(x) = 1/2x
f(x+h)-f(x)
= (2x -2x-2h)/2x(2x+2h)
= -2h/(4x^2+4xh)
divide by h
= -2/(4x^2+ 4xh)
let h--->0
= -2/4x^2
= -1/2x^2
Use the definition of derivative: lim(as h approaches 0) (f(x+h)-f(x)/(h) to find
f(x)=(1)/(2x).
1 answer