Home
Class 12
MATHS
Let lim(xto1) (x^(a)-ax+a-1)/((x-1)^(2))...

Let `lim_(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a)`. Then the value of `f(4)` is_________.

A

4

B

3

C

6

D

2

Text Solution

Verified by Experts

The correct Answer is:
`(6)`
Put `x=1+h`. Then,
`f(a)=underset(hto0)lim((1+h)^(a)-a(1+h)+a-1)/(h^(2))`
`=underset(hto0)lim((1+ah+(a(a-1))/(2!)h^(2)+...)-a-ah+a-1)/(h^(2))`
`:.f(a)=(a(a-1))/(2)`
`:.f(4)=6`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Archives JEE MAIN|8 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise Archives JEE ADVANCED|2 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Let ("lim")_(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

Let lim_(xto1)(x^(a)-ax+a-1)/((x-1)^(2))=f(a) . The value of f(101) equals

If lim_(xto1) (1+ax+bx^(2))^((e)/((x-1)))=e^(3) , then the value of bc is _________.

lim_(xto1)(sqrt(1-cos2(x-1)))/(x-1) ,

Evaluate lim_(xto1) (a^(x-1)-1)/(sinpix).

Let f:R in R be a continuous function such that f(1)=2. If lim_(x to 1) int_(2)^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is

Evalaute lim_(xto1) (1+logx-x)/(1-2x+x^(2))

Evaluate lim_(xto1) (x^(4)-sqrt(x))/(sqrt(x)-1) .

6. lim_(xto1)(1-x^2)^(1/log(1-x))

The value of lim_(xto1) (2-x)^(tan((pix)/(2))) is

CENGAGE ENGLISH-LIMITS-Numerical Value Type
  1. The value of lim(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50))) is .

    Text Solution

    |

  2. If L= lim(xto2) (root(3)(60+x^(2))-4)/(sin(x-2)), then the value of 1/...

    Text Solution

    |

  3. The value of lim(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x) is .

    Text Solution

    |

  4. The value of lim(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))] is .

    Text Solution

    |

  5. If L= lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^...

    Text Solution

    |

  6. The value of lim(x to oo ) (log(e)(log(e)x))/(e^(sqrt(x))) is . (a) π...

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. The value of lim(x to oo ) (x-x^(2)log(e)(1+(1)/(x))) is .

    Text Solution

    |

  9. Let S(n)=1+2+3+...+n " and " P(n)=(S(2))/(S(2)-1).(S(3))/(S(3)-1).(S(4...

    Text Solution

    |

  10. If lim(xto1)(asin(x-1)+bcos(x-1)+4)/(x^(2)-1)=-2, then |a+b| is.

    Text Solution

    |

  11. Let lim(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a). Then the value of f(4) ...

    Text Solution

    |

  12. Number of integral values of k for which lim(xto1) sin^(-1)((k)/(log...

    Text Solution

    |

  13. If lim(xto1) (1+ax+bx^(2))^((e)/((x-1)))=e^(3), then the value of bc i...

    Text Solution

    |

  14. Let f''(x) be continuous at x=0 If lim(xto0) (2f(x)-3af(2x)+bf(8x))/...

    Text Solution

    |

  15. If L=lim(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx), then the value of 1//...

    Text Solution

    |

  16. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

    Text Solution

    |

  17. If lim(xto0) [1+x+(f(x))/(x)]^(1//x)=e^(3), then the value of ln(lim(x...

    Text Solution

    |

  18. The largest value of the non-negative integer a for which lim(xto1) ...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. Let alpha,betainR be such that lim(xto0) (x^(2)sin(betax))/(alphax-sin...

    Text Solution

    |