Home
Class 12
MATHS
underset(trarra)lim(inta^tf(x)dx-((t-a)/...

`underset(trarra)lim(int_a^tf(x)dx-((t-a)/2)(f(t)-f(a)))/(t-a)^3`

Text Solution

Verified by Experts

4
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos

  • DETERMINATES

    PATHFINDER|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

underset(xrarr(pi//4))lim( int_2^(sec^2x)(f(t)dt))/(x^2-(pi)^2/16 equals

Statement -I : underset(xrarroo)"lim"(1^(2)/(x^(3))+(2^(2))/(x^(3))+3^(2)/(x^(3))+......+x^(2)/(x^(3)))= underset(xrarroo)"lim"(1^(2))/(x^(3))+underset(xrarroo)"lim"(2^(2))/(x^(3))+....+underset(xrarroo)"lim"(x^(2))/(x^(3))=0 Statement - II : underset(xrarra)"lim"{f_(1)(x)+f_(2)(x)+....+f_(n)(x)}=underset(xrarra)"lim"f_(1)(x)+underset(xrarra)"lim"f_(2)(x)+...+underset(xrarra)"lim"f_(n)(x)"

If f(x) is a differentiable function in the interval (0, oo) such that f(1)=1 and underset(t to x)lim(t^(2)f(x)-x^(2)f(t))/(t-x)=1 , for each x gt 0 then f((3)/(2)) is equal to

The value of underset(xrarr2)lim int_2^x (3t^2)/(x-2) dt is

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

If lim_(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2), then find the value of f'(0).

Investigate for maxima and minima of the function f(x) =int_(1)^(x)[2(t-1)(t-2)^(3)+3(t-1)^(2)(t-2)^(2)]dt .

lim_(trarr0) int_(0)^(2pi)(|sin(x+t)-sinx|)/(|t|)dx equals

The function f(x)=underset(-1)overset"x"intt(e^t-1)(t-1)(t-2)^3(t-3)^5 dt has a local minimum at 'x' equal to

Let f: RR to RR be a continuous odd function, which vanishes exactly at one point and f(1)=(1)/(2) . Suppose that F(x)=int(-1)^(x)f(t)dt for all x in[-1,2] and G(x)=int_(-1)^(x)t|f(ft)|dt" for all "x in[-1,2]." If "underset(xto1)lim(F(x))/(G(x))=(1)/(14) then the value of f((1)/(2)) is-

PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. If int(e^x-1)/(e^x+1)dx= f(x) +c, then find f(x).

    Text Solution

    |

  2. intx^2e^(x^3)cos(e^(x^3)) dx is equal to

    Text Solution

    |

  3. underset(trarra)lim(inta^tf(x)dx-((t-a)/2)(f(t)-f(a)))/(t-a)^3

    Text Solution

    |

  4. Evaluate :underset(nrarrinfty)lim((1^m+2^m+...+n^m)/n^(m+1))

    Text Solution

    |

  5. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

    Text Solution

    |

  6. The value of underset(nrarrinfty)limn{1/(3n^2+8n+4)+1/(3n^2+16n+16)+.....

    Text Solution

    |

  7. The value of underset(nrarrinfty)lim1/n^2{sin^3(pi)/(4n)+2sin^3 (2pi)/...

    Text Solution

    |

  8. The value of (n!)/((n-2)!) ia

    Text Solution

    |

  9. The value of int(-2)^2 (sin^2x)/([x/pi]+1/2) dx where [x] denotes the ...

    Text Solution

    |

  10. If I=int(pi/6)^(pi/6) (pi+4x^5)/(1-sin(absx+pi/6))dx then I equals

    Text Solution

    |

  11. I=int(-2)^2(abs(1-x^4))dx then I equals

    Text Solution

    |

  12. I=int-1^1([x^2]+log((2+x)/(2-x))dx....(1) where [x] denotes the greate...

    Text Solution

    |

  13. if f(x) is a function such that f(x+k)=f(x) for K in I^+ and I=int0^k...

    Text Solution

    |

  14. let T le0 be a fixed real number suppose f is continuous function such...

    Text Solution

    |

  15. ifI=int0^(pi/2)( sin8xlog(cotx))/(cos2x)dx then I equals

    Text Solution

    |

  16. ifI=int(1/3)^3 1/xsin (1/x-x)dx then I equals

    Text Solution

    |

  17. if b gt a and I=inta^b dx/(sqrt((x-a)(b-x) then I equals

    Text Solution

    |

  18. if I=int0^(pi/2) dx/(5+3sinx)=lambdatan^(-1)(1/2) then value oflambda ...

    Text Solution

    |

  19. if I=int(1/e)^e abslogx dx/x^2 then I equals

    Text Solution

    |

  20. The natural number nle5 for which In=int0^1 e^x(x-1)^n dx=16-6e is

    Text Solution

    |