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Let ((e^(x)-1)^(2))/(sin((x)/(a))log(1+(...

Let `((e^(x)-1)^(2))/(sin((x)/(a))log(1+(x)/(4)))" for "x ne 0 and f(0)=12.` If f is continuous at x = 0, then the value of a is equal to

A

1

B

`-1`

C

3

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(0)=lim_(x to 0)((e^(x)-1)^(2))/(sin((x)/(a))log(1+(x)/(4)))`
`rArr 12=lim_(x to 0)((e^(x)-1)/(x))^(2)*((x)/(a)*a)/("sin"(x)/(a))*((x)/(4)*4)/("log"(1+(x)/(4)))`
`rArr 12=1^(2)*a*4`
`therefore a = 3`
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