Question

lim as h ->0 of 1/h ln ((2+h)/2) is?

Answer 1

ur question just similar to find derivative of f(x) = ln(2)
do u know derivative of constanta will be .... ?

Answer 2

use L'Hopitals Rule, if the limit is indeterminate,
\[\lim_{x \rightarrow 0}\frac{ f(x) }{ g(x) } = \lim_{x \rightarrow 0}\frac{ f'(x) }{ g'(x) }\]so,
\[\lim_{h \rightarrow 0}\frac{ \ln(\frac{ 2+h }{ 2 }) }{ h }=\lim_{h \rightarrow 0}\frac{ (\frac{ 2 }{ 2+h })(\frac{ 1 }{ 2 }) }{ 1 }\]\[=\frac{ 1 }{ 2 }\]