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If the function f(x)=((e^(kx)-1)tankx)/(...

If the function `f(x)=((e^(kx)-1)tankx)/(4x^(2)),x ne 0`
`=16" "x=0`
is continuous at x=0, then k= . . .

A

`pm (1)/(8)`

B

`pm 4`

C

`pm 2`

D

`pm 8`

Text Solution

Verified by Experts

The correct Answer is:
D
We have function
`f(x) = ((e^(kx) -1)tan kx)/(4x^(2)) , x ne =0`
` 16 , x = 0`
is continous at x = 0
`therefore underset( x to 0)(lim)((e^(kx)-1)tan kx)/(4x^(2)) = 16 ((0)/(0) "from")`
` rArr underset(x to 0)(lim) ((e^(kv) -1)/(kx)) ((tan kx)/(kv)) xx (k^(2))/(4) = 16`
` rArr (k^(2))/(4) = 16 rArr k^(2) = 64 rArr k - pm 8`
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