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Evaluate lim(xto1) ("cos"(pi)/(2)x)/(1-s...

Evaluate `lim_(xto1) ("cos"(pi)/(2)x)/(1-sqrt(x))`

A

-1

B

1

C

0

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
`pi`
`underset(xto1)lim("cos"(pi)/(2)x)/(1-sqrt(x))" "`(form 0/0)
`=underset(xto1)lim((-pi)/(2)"sin"((pi)/(2)x))/(-(1)/(2sqrt(x)))`
`=((pi)/(2)xx1)/((1)/(2sqrt(1)))=(pi)/(2)xx2=pi`
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