Home
Class 12
MATHS
Let alpha and beta be the distinct roo...

Let ` alpha and beta ` be the distinct root of ` ax^(2) + bx + c=0 ` then` lim_(x to 0) (1- cos (ax^(2)+ bx+c))/((x-alpha)^(2))` is equal to

A

0

B

`1/2 (alpha -beta)^(2)`

C

`a^(2)/2 (alpha-beta)^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    DISHA PUBLICATION|Exercise Exercise- 1 : Concept Builder (Topic 4)|15 Videos
  • JEE MAIN - 2019 (HELD ON: 9TH APRIL 2019(MORNING SHIFT))

    DISHA PUBLICATION|Exercise MCQs|30 Videos
  • LINEAR INEQUALITIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0 then underset(x to alpha)(Lt) (1 - cos (ax^(2) + bx + c))/((x - alpha)^(2)) equal to

If alpha,beta are the distinct roots of x^(2)+bx+c=0 , then lim_(x to beta)(e^(2(x^(2)+bx+c))-1-2(x^(2)+bx+c))/((x-beta)^(2)) is equal to

If alpha and beta be the roots of ax^(2)+bx+c=0 then lim_(x rarr beta)(1-cos(ax^(2)+bx+c))/((x-beta)^(2))lim is

Let alpha and beta be the roots of the equation ax^(2)+bx+c=0 then lim_(x rarr beta)(1-cos(ax^(2)+bx+c))/((x-beta)^(2))

If alpha is repeated roots of ax^(alpha)+bx+c=0 then lim_(x rarr a)(tan(ax^(2)+bx+c))/((x-alpha)^(2)) is

Ifa alpha and beta be the roots of ax^(2)+bx+c=0, then lim_(x rarr alpha)(1+ax^(2)+bx+c)^((1)/(x-a)) is equal to

If alpha, beta are the zeroes of ax^(2)+bx+c , then evaluate : lim_(x to beta)(1-cos(ax^(2)+bx+c))/(x-beta)^(2) .

If alpha is a repeated root of ax^2+bx +c=0 , then lim_(xrarralpha)(sin(ax^2+bc+c))/(x-alpha)^2 is equal to

DISHA PUBLICATION-LIMITS AND DERIVATIVES-Exercise -2 : Concept Applicator
  1. lim(x->0)((cosx)^(1/2)-(cosx)^(1/3))/(sin^2x) is

    Text Solution

    |

  2. lim(x->0)((cosx)^(1/2)-(cosx)^(1/3))/(sin^2x) is

    Text Solution

    |

  3. Let alpha and beta be the distinct root of ax^(2) + bx + c=0 then ...

    Text Solution

    |

  4. If underset(x to 1)lim (ax^(2)+bx+c)/((x-1)^(2))=2" then "underset(x t...

    Text Solution

    |

  5. Evaluate underset(x to pi/4)lim (1-sin 2x)/(1+cos 4x)

    Text Solution

    |

  6. For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+....x^(2)/2+x+1, f...

    Text Solution

    |

  7. The value of lim(xto0)((4^x-1)^3)/(sin.(x^2)/(4)log(1+3x)),is

    Text Solution

    |

  8. If f(x) + f(y) = f((x+y)/(1-xy)) for all x, y in R (xy ne 1) and under...

    Text Solution

    |

  9. Evaluate underset(xto2)lim(x^(2)-x-2)/(x^(2)-2x-sin(x-2)).

    Text Solution

    |

  10. underset(n to oo)lim {1/(1-n^(2))+(2)/(1-n^(2))+....+(n)/(1-n^(2))} is...

    Text Solution

    |

  11. If zr=cos(pialpha)/(n^2)+isin(ralpha)/(n^2), where r=1,2,3....,n, then...

    Text Solution

    |

  12. If f(x)={{:(,|x|+1, x lt 0),(, 0,x=0),(,|x|-1, x gt 0):}" then "unders...

    Text Solution

    |

  13. The value of underset(theta to -pi/4)lim (cos theta +sin theta)/(theta...

    Text Solution

    |

  14. Let f(2)=4 and f'(2)=4. Then lim(x->2)(xf(2)-2f(x))/(x-2) is equal to

    Text Solution

    |

  15. The integer n for which lim(x rarr 0) ((cos x-1) ( cos x - e^x))/x^n i...

    Text Solution

    |

  16. The value f underset(x to pi/2)lim [1^(1//cos^(2)x)+2^(1//cos^(2) x)+....

    Text Solution

    |

  17. The value of underset(x to 2)lim (sqrt(1+sqrt(2+x))-sqrt3)/(x-2) is

    Text Solution

    |

  18. (lim)(xvec0)(sin(picos^2x))/(x^2) is equal to (1) pi/2 (2) 1 (3) ...

    Text Solution

    |

  19. If underset(x to 0)lim (x^(-3) sin 3x+ax^(-2) +b) exists and is equal ...

    Text Solution

    |

  20. If d/(dx)((1+x^4+x^8)/(1+x^2+x^4))=ax^3+bx,then

    Text Solution

    |