Home
Class 12
MATHS
Let f(a) = g(a) = k and their n^(th) ord...

Let f(a) = g(a) = k and their `n^(th)` order derivatives exist and are not equal for some `n in N`, further if `lim_(x rarr a) (f(a)g(x)-f(a)-g(a) f(x)+g(a))/(g(x)-f(x)) = 4` then the value of k is

A

0

B

4

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

Let f(x), g(x) be differentiable functions and f(1) = g(1) = 2, then : lim_(x rarr 1) (f(1) g(x) - f(x) g(1) - f(1) + g(1))/(g(x) - f(x)) equals :

It is given that f^(')(a) exists, then lim_(x rarr a) (x f(a) - a f(x))/(x-a) is equal to

int (f(x).g^(')(x)-f^(')(x)g(x))/(f(x).g(x)).[log g(x)-log f(x)]dx =

If the function f(x)= x^(3)+e^(x/2) and g(x) = f^(-1)(x) then the value of g^(')(1) is

If f(a)=2,f'(a)=1,g(a)=-3,g'(a)=-1 then Lim_(xtoa)(f(a)g(x)-f(x)g(a))/(x-a)=

int f(x) dx = g(x) , then int f(x)g(x) dx =

If f(x) is an odd function and lim_(x rarr 0) f(x) exists, then lim_(x rarr 0) f(x) is

If d/(dx) f(x) = g (x) , then int_a^b f(x) g(x) dx is:

If f(a) = 2 , f ' (a) = 1 , g (a) = -1 , g'(a) = 2 , then lim_(x to a) (g (x) * f (a) - g (a) * f(x))/( x- a) is equal to

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(2)=4 and f'(2)=4. Then lim(xto2)(xf(2)-2f(x))/(x-2) is given b...

    Text Solution

    |

  2. lim(x rarr oo) (logx^(n)-[x])/([x]), where n in N and [.] denotes the ...

    Text Solution

    |

  3. Let f(a) = g(a) = k and their n^(th) order derivatives exist and are n...

    Text Solution

    |

  4. Let f:R to R be a positive increasing function with lim(x to oo) (f(3x...

    Text Solution

    |

  5. lim(x rarr 0) x^(2). sin (pi/x) is

    Text Solution

    |

  6. If 0 lt x lt y, then lim(n rarroo)(y^(n)+x^(n))^(1/n) is equal to

    Text Solution

    |

  7. The value of lim(x rarr 0) (e^(x)-e^(sinx))/(2 (x-sinx))=

    Text Solution

    |

  8. If f(x) = {((sin(1+[x]))/([x]), for [x] ne 0),(0, for [x] = 0):} , wh...

    Text Solution

    |

  9. If f : R rarr R is defined by f(x) = [x-3]+|x-4| for x in R, then lim(...

    Text Solution

    |

  10. lim(x rarr 0) ((1-e^(x))sin x)/(x^(2)+x^(3)) =

    Text Solution

    |

  11. lim(x rarr 0) (sqrt(1+x)-1)/x =

    Text Solution

    |

  12. If f(x) = [((sin [x])/([x]), [x] ne 0),(0, [x] = 0)], then lim(x rarr ...

    Text Solution

    |

  13. The value of lim(x rarr k^(-)) x -[x], where k is an integer, is

    Text Solution

    |

  14. The value of lim(x rarr 0) (1-cos(1-cosx))/(x^(4)) is

    Text Solution

    |

  15. lim(x rarr 3)[x] =

    Text Solution

    |

  16. lim(x rarr 1) (x^(8)-2x+1)/(x^(4)-2x+1) =

    Text Solution

    |

  17. If f(x) = sqrt((x-sinx)/(x+cos^(2)x)), then lim(x rarr oo) f(x) =

    Text Solution

    |

  18. lim(n rarr oo) (1+(sin) a/n)^(n) equals

    Text Solution

    |

  19. lim(x rarr 0) (4^(x)-1)/(3^(x)-1) =

    Text Solution

    |

  20. The value of lim(n rarr oo){1/1.3+1/3.5+1/5.7+...+1/((2n+1)(2n+3))} is

    Text Solution

    |