If f(a) = 0 and f '(a) = 6, find lim as h->0 f(a+h)/2h

the answer should be 3, but I don't know how to get that, help!

ƒ(a+0) / 2(0) = ƒ(a) / 0 = 0/0, an indeterminate form

Hence, by L' Hopital's Rule,

.. lim (h→0) [ ƒ(a+h) ] / (2h)

= lim (h→0) d/dh[ ƒ(a+h) ] / d/dh( 2h )

= lim (h→0) [ ƒ'(a+h) ] / 2(1)

= ƒ'(a+0) / 2

= ƒ'(a) / 2

= 6/2

= 3 ........................................… Ans.
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