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"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan...

`"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3))`. Then find the value of f'(0).

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(pi)`
`'f(0)=underset(xrarr0)lim(f(x)-f(0))/(x-0)`
`=underset(xrarr0)lim((2^(x)+2^(-x))(sin x)/(x)sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(2))`
`=(2xx1sqrt(tan^(-1)1))/((0+0+1)^(3))`
`=sqrt(pi)`
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