lim x(2^x-1)/(1-cosx) x->0

Asked by Rohan Astik | 30th Apr, 2013, 04:05: PM

Expert Answer:

lim       x(2^x-1)/(1-cosx)
x->0
 
lim      (x/2sin(x/2)^2 ) * [(2^x-1)/x] *x
x->0
 
lim     (1/2)*4 ((x/2)^2/sin(x/2)^2 ) * [(2^x-1)/x]
x->0
= 2*1*ln2
= 2ln2

Answered by  | 1st May, 2013, 07:26: PM

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