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If lim(x to 1)((e^(k)-1)sin kx)/(x^(2))...

If `lim_(x to 1)((e^(k)-1)sin kx)/(x^(2))=4`, then k is equal to

A

2

B

`-2`

C

`pm 2`

D

`pm 4`

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to 0) ((e^(kx)-1)sin kx)/(x^(2))=4`
`rArr lim_(x to 0) (e^(kx)-1)/(x)lim_(x to 0)(sinkx)/(x)=4`
`rArr k*lim_(x to 0)(e^(kx)-1)/(kx)*k lim_(x to 0)(sin kx)/(kx)=4`
`rArr k^(2)=4`
`rArr k =pm 2`
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Knowledge Check

  • Evaluate, lim_(x to 1) (x^(4)-1)/(x-1)=lim_(x to k) (x^(3)-k^(3))/(x^(2)-k^(2)) , then find the value of k.

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  • lim_(x to 0) (1+ sin x)^(1//x^(2)) is equal to:

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  • If f(x)=(sin(e^(x-2)-1))/(In(x-1)) then lim_(xto2)(x) is equal to ?

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