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The value of f(0) so that f(x) = ((4x^...

The value of f(0) so that ` f(x) = ((4x^(x)-1)^(3))/(sin(x/4)log(1+(x^(2))/3)) , x != 0 , ` is continuous everywhere in R, is

A

`3(log 4)^(3)`

B

`4(log 4)^(3)`

C

`12(log 4)^(3)`

D

`15(log 4)^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to 0) f(x)=lim_(x to0) ((4^(x)-1)^(3)x^(3))/(x^(3))* ((1)/("sin"(x)/(4)*(x)/(4)))/((x)/(4))*((1)/(log(1+(x^(2))/(3))*(x^(2))/(3)))/((x^(2))/(3))`
`=((4^(x)-1)/(x))^(3)*(1)/(((sinx//4)/((x)/(4))))*(1)/((x)/(4))*(x^(3))/((x^(2))/(3)-(x^(4))/(9)+(x^(6))/(27)-...)`
`rArr f(0)=12(log 4)^(3)`
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