Home
Class 12
MATHS
It is given that f^(')(a) exists, then l...

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

A

`f(a)-af^(')(a)`

B

`f^(')(a)`

C

`-f^(')(a)`

D

`f(a) + af^(')(a)`

Text Solution

Verified by Experts

The correct Answer is:
A
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

If f(2) = 4 and f^(')(2) =1 then lim_(x rarr 2) (x f(2)-2f (x))/(x-2)

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

If f(2) = 2 and f^(')(2) = 1 , then lim_(x rarr 2) (2x^(2)-4 f(x))/(x-2) =

Find lim_(xrarr5)f(x) , where f(x)=|x|-5

If f : R rarr R is defined by f(x) = [x-3]+|x-4| for x in R , then lim_(x rarr 3^(-)) f(x) is equal to

If f(9) =9, f^(')(9) = 4 , then lim_(x rarr 9)(sqrt(f(x))-3)/(sqrtx - 3) =

If f(1) =1 and f^(')(1) =2 then lim_(x rarr 1) (sqrt(f(x))-1)/(sqrt(x) -1) =

If function f(x) is differentiable at x=a , then lim_(xtoa)(x^(2)f(a)-a^(2)f(x))/(x-a) is :

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x) = {((tanx - cotx)/(x-pi/4), xne pi/4),(a, x = pi/4):}. The va...

    Text Solution

    |

  2. The value of f(0), so that the function f(x) = (sqrt(a^(2)-ax+x^(2))-s...

    Text Solution

    |

  3. The function f(x)=1+|sinx| is :

    Text Solution

    |

  4. The range of the function f(x)=[x]-x , where [x] denotes the greatest ...

    Text Solution

    |

  5. Let f((x+y)/2) = (f(x)+f(y))/2 for all real values of x and y. If f^('...

    Text Solution

    |

  6. Let f : R rarr R be a function defined by f(x) = max {x,x^(3)}. The se...

    Text Solution

    |

  7. The domain of the derivative of the function f(x) = {(tan^(-1)x, |x|le...

    Text Solution

    |

  8. lim(h rarr 0) (f(2h+2+h^(2))-f(2))/(f(h-h^(2)+1)-f(1)) given that f^('...

    Text Solution

    |

  9. If f(x) is differentiable increasing function, then lim(x to 0) (f(x^(...

    Text Solution

    |

  10. If f(x) is continuos and differentiable function such that f(1/n) = 0 ...

    Text Solution

    |

  11. Let f(x+y) = f(x).f(y), forall, x, y. Suppose f(5) =2, f^(')(0) = 3 th...

    Text Solution

    |

  12. If f(x) = {(x-5,x le1),(4x^(2)-9, 1ltxlt2),(3x+4, x ge2):} then f^(')(...

    Text Solution

    |

  13. If f(2) = 4 and f^(')(2) =1 then lim(x rarr 2) (x f(2)-2f (x))/(x-2)

    Text Solution

    |

  14. If f(x+y) = 2f(x) f(y) for all x,y where f^(')(0) = 3 and f(4) =2, the...

    Text Solution

    |

  15. If x+4|y| = 6y, then y as a function of x is

    Text Solution

    |

  16. If f(x+y)=f(x)f(y) and f(x)=1+"xg(x) G(x)", where lim(xto0)g(x)=a and...

    Text Solution

    |

  17. The function f(x)=x^(3)-3x is :

    Text Solution

    |

  18. Let f(x)=x(x-sqrt(x+1)). Then :

    Text Solution

    |

  19. It is given that f^(')(a) exists, then lim(x rarr a) (x f(a) - a f(x))...

    Text Solution

    |

  20. Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x), where g(x) is continuous. ...

    Text Solution

    |