Home
Class 12
MATHS
Let f: RvecR be a differentiable functio...

Let `f: RvecR` be a differentiable function having `f(2)=6,f^(prime)(2)=1/(48)dot` Then evaluate `("lim")_(xvec2)int_6^(f(x))(4t^3)/(x-2)dt`

A

18

B

12

C

36

D

24

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -2 (LEVEL-II)|11 Videos

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -3|55 Videos

  • DEFINITE INTEGRATION

    MOTION|Exercise ELEMENTRAY EXERCISE|47 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-II)|6 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R be a differentiable function having f(2)=6,f'(2)=(1)/(48). Then evaluate lim_(x rarr2)int_(6)^(f(x))(4t^(3))/(x-2)dt

Let f:R to R be a differentiable function having f(2)=6,f'(2) =(1)/(12) . Then, lim_(x to 2)overset(f(x))underset(6)int(4t^(3))/(x-2)dt , equals

Let f:R to R be a differentiable function such that f(2)=2 . Then, the value of lim_(xrarr2) int_(2)^(f(x))(4t^3)/(x-2) dt , is

Suppose f:R rarr R is a differentiable function and f(1)=4. Then value of (lim)_(x rarr1)(int_(4)^(f(x))(2t))/(x-1)dt is

Let f : R to R be a differentiable function and f(1) = 4 . Then, the value of lim_(x to 1)int_(4)^(f(x))(2t)/(x-1)dt is :

Let f : R to R be a continuously differentiable function such that f(2) = 6 and f'(2) = 1/48 * If int_(6)^(f(x)) 4t^(3) dt = (x-2) g(x)" than" lim_( x to 2) g(x) is equal to

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) for all x ,\ y > 0. If f^(prime)(1)=1 then find f(x)dot

MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If int0^11 (11^x)/(11^([x])) dx=k/(log 11) then value of k is (where [...

    Text Solution

    |

  2. Let Tgt0 be a fixed real number. Suppose f is a cintinuous function s...

    Text Solution

    |

  3. Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1...

    Text Solution

    |

  4. The value of lim(xto0) (int(0)^(x^2)sec^2t dt)/(x sin x) dx , is

    Text Solution

    |

  5. underset( x to 0) lim ( int(0)^(x^(2)) cos^(2)t" "dt)/(x sin x) = ...

    Text Solution

    |

  6. If int0^y cos t^2\ dt = int0^(x^2)\ sint/t \ dt, then dy/dx is equal t...

    Text Solution

    |

  7. let f(x)=int(t^2-t+1)dt,AA x in (3,4), then the difference between th...

    Text Solution

    |

  8. Ifint(sinx)^1t^2f(t)dt=1=1-s inx ,w h e r ex in (0,pi/2), then find t...

    Text Solution

    |

  9. The smallest interval [a,b] such that overset(1)underset(0)int (1)/...

    Text Solution

    |

  10. Given that n is odd and m is even integer. the value of int (0) ^(x ) ...

    Text Solution

    |

  11. underset(n to oo)"lim"underset(r=1)overset(n)sum((r^(3))/(r^(4) + n^(4...

    Text Solution

    |

  12. underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-...

    Text Solution

    |

  13. lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

    Text Solution

    |

  14. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

    Text Solution

    |

  15. Lim(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+...

    Text Solution

    |

  16. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

    Text Solution

    |

  17. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

    Text Solution

    |

  18. Let I (1) = int (1) ^(2) (dx )/(sqrt(1 + x ^(2))) and I (2) = int (1) ...

    Text Solution

    |

  19. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

    Text Solution

    |

  20. If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, I (2) = int (0) ^(1) 2 ^(x ^(3...

    Text Solution

    |