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lim(trarr0) int(0)^(2pi)(|sin(x+t)-sinx|...

`lim_(trarr0) int_(0)^(2pi)(|sin(x+t)-sinx|)/(|t|)dx` equals

A

a) 2

B

b) 4

C

c) 1/4

D

d) 1

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(trarr0)(lim)int_(0)^(2pi)|(sin(x+t)-sinx)/(t)|dx`
`=int_(0)^(2pi)(underset(trarr0)(lim)|(2cos(x+(t)/(2))sin(t)/(2))/(t)|)dt`
`=int_(0)^(2pi)|cosx|dx=4`
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