Home
Class 12
MATHS
Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(...

Let `f(x)=int_2^x(dt)/(sqrt(1+t^4))a n dg(x)` be the inverse of `f(x)` . Then the value of `g'(0)`

A

`1`

B

`17`

C

`sqrt(17)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=int_(2)^(x)(dt)/(sqrt(1+t^(4)))`
`implies f'(x)=1/(sqrt(1+x^(4)))=(dy)/(dx)`
Now `g'(x)=(dx)/(dy)=sqrt(1+x^(4))`
when `y=0`, ie. `int_(2)^(x)(dt)/(sqrt(1+t^(4)))=0` then `x=2`
`:. g'(0)=sqrt(1+16)=sqrt(17)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise LC_TYPE|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CAE_TYPE|88 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=int_(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x) . Then the value of 4 (g''(x))/(g(x)^(2)) is________.

Let f(x)=(1)/(1+x^(2)) and g(x) is the inverse of f(x) ,then find g(x)

Let f(x) = int_2^x f(t^2-3t+2) dt then

Let f(x)=int(x^2dx)/((1+x^2)(1+sqrt(x^2+1)))a n df(0)=0. Then value of f(1) will be

Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), then g'(3) equals _

Let f(x)=1/x^2 int_4^x (4t^2-2f'(t))dt then find the value of 9f'(4)

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

Let f(x)=x^(x),x in (0,oo) and let g(x) be inverse of f(x), then g'(x) must be

f(x)=int_1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

If f(x)=int_0^x(sint)/t dt ,x >0, then

CENGAGE PUBLICATION-DEFINITE INTEGRATION -SCQ_TYPE
  1. If g(x)=int0^x(|sint|+|cost|)dt ,then g(x+(pin)/2) is equal to, where...

    Text Solution

    |

  2. Ifx=intc^(sint)sin^(-1)z dz ,y=intk^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)...

    Text Solution

    |

  3. Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Th...

    Text Solution

    |

  4. If f(x) is differentiable and int0^(t^2) x f(x) dx=2/5t^5, then f(4/(2...

    Text Solution

    |

  5. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to -...

    Text Solution

    |

  6. A function f is continuous for all x (and not everywhere zero) such th...

    Text Solution

    |

  7. lim(x->0)1/x[inty^a e^(sin^2t)dt-int(x+y)^a e^(sin^2t)dt] is equal to

    Text Solution

    |

  8. Let f(x) =int1^x e^t/tdt,x in R^+ . Then complete set of valuesof x f...

    Text Solution

    |

  9. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

    Text Solution

    |

  10. If f(x)=1+1/x int1^x f(t) dt, then the value of f(e^-1) is

    Text Solution

    |

  11. If [f((sqrt(3))/2)] is [.] denotes the greatest integer function)

    Text Solution

    |

  12. f(x) is continuous function for all real values of x and satisfies int...

    Text Solution

    |

  13. The value of int(1/e)^tanx(tdt)/(1+t^2)+int(1/e)^cotxdt/(t(1+t^2) is

    Text Solution

    |

  14. lim(xto oo) (int(0)^(x)tan^(-1)t\ dt)/(sqrt(x^(2)+1)) is equal to

    Text Solution

    |

  15. A function is defined by f(x) = int0^pi cos t cos(x-t)dt,0 <= x <= 2 p...

    Text Solution

    |

  16. If f' is a differentiable function satisfying f(x)=int(0)^(x)sqrt(1-f^...

    Text Solution

    |

  17. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

    Text Solution

    |

  18. The value of the integral int0^1e^(x^2) dx lies in the interval (a) (0...

    Text Solution

    |

  19. Given that f satisfies |f(u)-f(v)|lt=|u-v| for u and v in [a , b]dot T...

    Text Solution

    |

  20. The value of the integral int0^oo(xlogx)/((1+x^2)^2)dx ,is (a)0 (...

    Text Solution

    |