Home
Class 12
MATHS
Suppose lim(xrarr0) (int(0)^(x)(t^(2) d...

`Suppose lim_(xrarr0) (int_(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx)=l`,
`p in N, p ge 2,a gt gt 0,rgt 0 and b ne 0`
If `l` exists and is non- zero, then

A

`b gt 1`

B

`0 lt b lt 1`

C

`b lt0`

D

`b=1`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|4 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|4 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Suppose lim_(xrarr0)(int_(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx)=l , p in N, p ge 2,a gt gt 0,rgt 0 and b ne 0 If p=3 and l=1, then the value of 'a' is equal to

Suppose lim_(x to 0)(int_(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx)=l , p in N, p ge 2,a gt gt 0,rgt 0 and b ne 0 If p=2 and a=9 and l exists , then the value of l is equal to

The value of lim_(x rarr0)(2int_(0)^(cos x ) cos^(-1) (t))/(2x- sin 2 x)dx is

The value of lim_(xrarr0)(1)/(x^(3)) int_(0)^(x)(tln(1+t))/(t^(4)+4) dt

underset(xrarr0)lim (sin4x)/(sin2x) is:

lim(x->0)(1/(x^5)int_0^xe^(-t^2)dt-1/(x^4)+1/(3x^2)) is equal to

Let lim_(T rarr infty) (1)/(T) int_(0)^(T) ( sin x + sin ax)^(2) dx =L , then

Let f(x)=int_(0)^(x)"cos" ((t^(2)+2t+1)/(5))dt,0>x>2, then

If (d)/(dx)(int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2)) sin^(2) tdt)=0, "find" (dy)/(dx).

Evaluate : lim_(x rarr 0)(sin ax)/(sin bx), a,b ne 0 .

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Passage Based Questions)
  1. Suppose lim(xrarr0) (int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- si...

    Text Solution

    |

  2. Suppose lim(xrarr0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx...

    Text Solution

    |

  3. Suppose lim(x to 0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sin...

    Text Solution

    |

  4. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

    Text Solution

    |

  5. Suppose f(x) and g(x) are two continuous function defined for 0 le xl...

    Text Solution

    |

  6. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

    Text Solution

    |

  7. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

    Text Solution

    |

  8. Evaluate int (0)^(1) 3x^2 dx

    Text Solution

    |

  9. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

    Text Solution

    |

  10. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  11. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  12. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  13. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

    Text Solution

    |

  14. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

    Text Solution

    |

  15. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

    Text Solution

    |

  16. Check the injectivity and surjectivity of the function sinx.

    Text Solution

    |

  17. The value of int(0)^(100)[ tan ^(-1)x] d x is equal to (where [.] den...

    Text Solution

    |