Home
Class 12
MATHS
"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)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.4|12 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.5|16 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.2|40 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If f:RtoR,f(x)=(sqrt(x^(2)+1)-3x)/(sqrt(x^(2)+1)+x) then find the range of f(x) .

If (x^2+x−2)/(x+3) -1) f(x) then find the value of lim_(x->-1) f(x)

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

If f (x)=((x+1)^(7)sqrt(1+x ^(2)))/((x^(2) -x+1)^(6)), then the value of f'(0) is equal to:

Draw the graph of f(x) = (sin x)/(sqrt(1 + tan^(2)x))- (cos x)/(sqrt(1 + cot^(2)x)) . Then find the range of f(x).

If f(x) = sqrt((1)/(tan^(-1)(x^(2)-4x + 3))) , then f(x) is continuous for

f(x)=|{:(cos x, x, 1),(2sin x, x^(2), 2x),(tan x, x, 1):}|." Then find the vlue of lim_(x to 0) (f'(x))/(x).

If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5

If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5

If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5