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Solution:
limh→0 f(5 + h) − f(5)/h = limh→0 [ 1/2(5+h) - 1/2(5)]/h
= limh→0 (1/2h)[(5 - (5+h)]/[5(5+h)]
= limh→0 (-h)/[(10h)(5+h)]
= limh→0 (-1)/[10(5+h)]
= (-1/50)
Summary:
The value of limh→0 f(5 + h) − f(5) all over h is (-1/50)