evaluate-lim-x-0-a-x-cos-t-t-dt-x-

Question Number 77182 by jagoll last updated on 04/Jan/20

evaluate \lim_{x \to 0} \frac{\underset{a}{\int^{x}} (\frac{\cos t}{t}) dt}{x} .

Commented by mathmax by abdo last updated on 05/Jan/20

i t h i n k t h a t a = 0 \dots

Answered by john santu last updated on 04/Jan/20

s u p p o s e F (t) i s a n t i d e r i v a t i v e

\int \frac{\cos t}{t} d t s u c h t h a t \frac{d F (t)}{d t} = \frac{\cos (t)}{t} .

n o w \lim_{x \to 0} \frac{F (t) \underset{a}{\overset{x}{∣}}}{x} = \lim_{x \to 0} \frac{F (x) - F (a)}{x}

w e a s s u m e t h a t F (0) - F (a) = 0

\lim_{x \to 0} \frac{F^{'} (x) - F^{'} (a)}{1} = F^{'} (0) - F^{'} (a)

b u t F^{'} (0) = \frac{\cos (0)}{0} u n d e f i n e d

i t h i n k i t p r o b l e m e r r o r .

Commented by jagoll last updated on 04/Jan/20

thanks sir . i will check my question

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