Let f(x) = 1/2x . compute lim_h→0 f(5 + h) − f(5) all over h.

Solution:

lim_h→0 f(5 + h) − f(5)/h = lim_h→0 [ 1/2(5+h) - 1/2(5)]/h

= lim_h→0 (1/2h)[(5 - (5+h)]/[5(5+h)]

= lim_h→0 (-h)/[(10h)(5+h)]

= lim_h→0 (-1)/[10(5+h)]

= (-1/50)

Given f(x) = 1/2x compute lim_h→0 f(5 + h) − f(5) all over h.

Summary:

The value of lim_h→0 f(5 + h) − f(5) all over h is (-1/50)