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Among (i) lim(xtooo) sec^(-1)((x)/(sinx)...

Among (i) `lim_(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim_(xtooo) sec^(-1)((sinx)/(x)).`

A

`0`

B

`(1)/(2sqrt(2))`

C

`(1)/(sqrt(2))`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xtooo)limsec^(-1)((x)/(sinx))=sec^(-1)((oo)/(sinoo))`
`=sec^(-1)((oo)/("any value between "-1" to "1))`
`=sec^(-1)(+-oo)=(pi)/(2)`
`underset(xtooo)limsec^(-1)((sinx)/(x))=sec^(-1)((sinoo)/(oo))`
`=sec^(-1)(("any value between "-1" to "1)/(oo))`
`=sec^(-1)0` = not defined
Hence, (i) exists but (ii) does not exist.
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CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
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