Home
Class 11
MATHS
If alpha and beta be the roots of the qu...

If `alpha` and `beta` be the roots of the quadratic equation `ax^2+bx+c=0` then evaluate
`lim_(xrarralpha)(1-cos(ax^2+bx+c))/((x-alpha)^2)`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If alpha,beta are the roots of the quadratic equation ax^2+bx+c=0 and 3b^2=16ac then

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 , then show that underset(xrarralpha)"lim"(1-cos(ax^(2)+bx+c))/((x-alpha)^(2))=(a^(2))/(2)(alpha-beta)^(2)

If alpha,beta are the roots of the quadratic equation ax^(2)+bx+c=0and3b^(2)=16ac then-

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0 and 3b^(2)=16 ac then

IF alpha and beta be the roots of the equation ax^2+bx+c=0 , find the values of alpha^2+beta^2

If one of the root of the quadratic equation ax^2+bx+c=0,(a!=0) be zero then

The roots of the equation ax^2+bx+c=0 are equal when-

IF alpha and beta be the roots of the equation ax^2+bx+c=0 , find the values of 1/alpha^3+1/beta^3

If the roots of the equation ax^2+bx+c=0(a!=0) be equal then

If the roots of the equation ax^(2)+bx+c=0(ane0) be equal, then

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Evaluate lim(xrarr0)(x-int0^(x) cost^2dt)/(x^3-6x)

    Text Solution

    |

  2. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

    Text Solution

    |

  3. If alpha and beta be the roots of the quadratic equation ax^2+bx+c=0 t...

    Text Solution

    |

  4. Let a=min{x^2+2x+3, x in R} and b=lim(thetararr0)(1-costheta)/(theta^2...

    Text Solution

    |

  5. If f(x)={(2x+3, "when x" lt 0),(0, "when x"=0),(x^2+3, "when x"gt 0):}...

    Text Solution

    |

  6. Let y=f(x) be defined parametrically as y=t^2+t|t|, x=2t-|t|, t in R, ...

    Text Solution

    |

  7. Let f(x) be a continuous function defined for 1 le x le 3. If f(x) tak...

    Text Solution

    |

  8. Find the points points of discontinuity of y=1/(u^2+u-2) where u=1/(x-...

    Text Solution

    |

  9. If f(x)=[x], where [.] denotes greatest integer function. Then check t...

    Text Solution

    |

  10. Let f(x)={({1+|sinx|}^(a//|sinx|), -pi//6ltxlt0),(b, x=0),(e^(tan2x...

    Text Solution

    |

  11. Discuss the continuity of f(x)=[tan^(-1)x]

    Text Solution

    |

  12. Examine the function, f(x)={(x-1, x lt 0),(1//4, x=0), (x^2-1, xg...

    Text Solution

    |

  13. Show the function, f(x)={((e^(1//x)-1)/(e^(1//x)+1), "when x" le 0),...

    Text Solution

    |

  14. A function f(x) is defined by, implies f(x)=f(x)={(([x^2]-1)/(x^2-1)...

    Text Solution

    |

  15. Discuss the continuity of the function, f(x)=lim(nrarrinfty)(log(2+x)...

    Text Solution

    |

  16. Discuss the continuity of f(x) where f(x)=lim(nrarrinfty)("sin" (pix)/...

    Text Solution

    |

  17. If f(x) be continuous function for all real values of x and satisfies,...

    Text Solution

    |

  18. Which of the following functions is differentiable at x=o ?

    Text Solution

    |

  19. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

    Text Solution

    |

  20. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

    Text Solution

    |