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_(xto2)int_6^(f(x))(4t^3)/(x-2)dt`

Text Solution

Verified by Experts

`lim_(xto2)int_(6)^(f(x))(4t^(3))/(x-2)dtlim_(xto2)(int_(6)^(f(x))4t^(3)dt)/(x-2)[0/0 "form"]`
`=lim_(xto2)(4(f(x))^(3)f'(x))/1`
(applying L' Hopital rule)
`=4(f(2))^(3)xxf'(2)`
`=4(6)^(3)xx1/48`
`=18`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLE_TYPE|20 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: R->R be a differentiable function having f(2)=6,f^(prime)(2)=1/(48)dot Then evaluate ("lim")_(x->2)int_6^(f(x))(4t^3)/(x-2)dt

The value of lim_(xto2)int_(2)^(x)(3t^(2))/(x-2)dt is

Let f : R rarr R be a differentiable function having f(2) = 6, f'(2) = (frac(1)(48)) . Then lim_(xrarr2)( int_2^f(x) f(4t^3)dt)/(x-2) is equals

Evaluate (lim)_(x to 4)int_4^x((4t-f(t)))/((x-4))dt

Let f:R to R be a differentiable function and f(1)=4 and f'(1)=2 , then the value of lim_(x to 1) int_(4)^(f(x))(2t)/(x-1)dt is -

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

If f(2)=4,f'(2)=4 , then evalute lim_(xto2)(xf(2)-2f(x))/(x-2) .

Let f: R → R be a one-one onto differentiable function, such that f(2)=1 and f^(prime)(2)=3. Then, find the value of (d/(dx)(f^(-1)(x)))_(x=1)

If f(2)=4,g(2)=9andf'(2)=2g'(2) , then evaluate lim_(xto2)(sqrt(f(x))-2)/(sqrt(g(x))-3) .

Let f(x) be a twice-differentiable function and f"(0)=2. The evaluate: lim_(x->0)(2f(x)-3f(2x)+f(4x))/(x^2)

CENGAGE PUBLICATION-DEFINITE INTEGRATION -JEE ADVANCED
  1. Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1...

    Text Solution

    |

  2. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e (22)/7-pi (b) 2/...

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

    Text Solution

    |

  6. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  8. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

    Text Solution

    |

  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  11. The value of int(-pi/2)^(pi/2) (x^2cosx)/(1+e^x) dx is equal to

    Text Solution

    |

  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  15. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  16. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

    Text Solution

    |

  17. Let f:(0,oo)rarrRR be given by f(x)=oversetxunderset(1/x)inte^((t+1/...

    Text Solution

    |

  18. The option(s) with the values of a and L that satisfy the following eq...

    Text Solution

    |

  19. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

    Text Solution

    |

  20. find the period of sin(x/2)-cos(x/3) is

    Text Solution

    |

  21. Let f: Rto(0,1) be a continuous function. Then, which of the following...

    Text Solution

    |