Home
Class 11
MATHS
It is given that f′ (a) exists, then lim...

It is given that f′ (a) exists, then `lim_(x->a)(xf(a)-af(x))/(x-a)`is equal to:

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    RD SHARMA ENGLISH|Exercise All Questions|269 Videos

  • ELLIPSE

    RD SHARMA ENGLISH|Exercise All Questions|100 Videos

Similar Questions

Explore conceptually related problems

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

If f(x) =x , x 0 then lim_(x->0) f(x) is equal to

If lim_(x->a)(f(x)/(g(x))) exists, then

If f (x) = x^(4) + 2x^(3) , them lim_(x to 2) (f(x) - f(2))/(x - 2) is equal to

If f is derivable at x =a,then underset(xto a ) lim( (xf(a) -af( x))/(x-a) )

If f(3)=6 and f'(3)=2, then lim_(x to 3) (xf (3)-3f(x))/(x-3) is given by

If f(x)=f(a+b-x), then int_(a)^(b) xf(x)dx is equal to

If f(4)= 4, f'(4) =1 then lim_(x to 4) 2((2-sqrtf(x))/ (2 - sqrtx)) is equal to

The value of lim_(h to 0) (f(x+h)+f(x-h))/h is equal to

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

RD SHARMA ENGLISH-DERIVATIVES-All Questions
  1. Differentiate the following function with respect of x" ":1/(a x^2+b x...

    Text Solution

    |

  2. Write the value of lim(x->c)(f(x)-f(c))/(x-c).

    Text Solution

    |

  3. It is given that f′ (a) exists, then lim(x->a)(xf(a)-af(x))/(x-a)is eq...

    Text Solution

    |

  4. If x<2, then write the value of d/(dx)(sqrt(x^2-4x+4))dot

    Text Solution

    |

  5. If pi/2 lt x lt pi, then find d/dx(sqrt((1+cos2x)/2))

    Text Solution

    |

  6. Write the value of d/(dx)(x \ |x|).

    Text Solution

    |

  7. Write the value of d/(dx){(x+|x|)|x|}dot

    Text Solution

    |

  8. If f(x)=|x|+|x-1| , write the value of d/(dx)(f(x)).

    Text Solution

    |

  9. Write the value of the derivative of f(x)=|x-1|+|x-3| \ at \ x = 2.

    Text Solution

    |

  10. If f(x)=(x^2)/(|x|), write d/(dx)(f(x))

    Text Solution

    |

  11. Write the value of d/(dx)(log|x|).

    Text Solution

    |

  12. If f(1)=1,f^(prime)(1)=2, then write the value of lim(x->1)(sqrt(f(x))...

    Text Solution

    |

  13. Write the derivative of f(x)=3 \ |2+x| at x=-3.

    Text Solution

    |

  14. If |x|<1 and y=1+x+x^2+x^3+... , then write the value of (dy)/(dx)dot

    Text Solution

    |

  15. Let f:R→R be a function defined by f(x)= \frac{ x ^ { 2 } -8 }{ ...

    Text Solution

    |

  16. If f(x)=(x-4)/(2sqrt(x)), then f^(prime)(1) is a. 5/4 b. 4/5 c. 1 d. 0

    Text Solution

    |

  17. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... , then (dy)/(dx)= a. y+1 b. y-...

    Text Solution

    |

  18. If f(x)=1-x+x^2-x^3+...-x^(99)+x^(100), then f^(prime)(1) equals a. 15...

    Text Solution

    |

  19. If y=(1+1/(x^2))/(1-1/(x^2)), then (dy)/(dx)= a. -(4x)/((x^2-1)^2) b. ...

    Text Solution

    |

  20. If y=sqrt(x)+1/(sqrt(x)), then (dy)/(dx) \ at \ x=1 is a. 1 b. 1/2 c....

    Text Solution

    |