Home
Class 12
MATHS
If f(x) is differentiable at x=a , find ...

If `f(x)` is differentiable at `x=a` , find `(lim)_(x->a)(x^2f(a)-a^2\ f(x))/(x-a)` .

Text Solution

AI Generated Solution

To find the limit \[ \lim_{x \to a} \frac{x^2 f(a) - a^2 f(x)}{x - a}, \] we can start by rewriting the expression in the limit. ...
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    RD SHARMA|Exercise Solved Examples And Exercises|403 Videos

  • DIFFERENTIAL EQUATION

    RD SHARMA|Exercise Solved Examples And Exercises|634 Videos

Similar Questions

Explore conceptually related problems

If f(x) is differentiable at x=a, find lim_(x rarr a)(x^(2)f(a)-a^(2)f(x))/(x-a)

If f(x) is differentiable at x=a, then lim_(x toa)(x^2f(a)-a^2f(x))/(x-a) is equal to

If f is differentiable at x=1, Then lim_(x to1)(x^2f(1)-f(x))/(x-1) is

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

let f(x) be differentiable at x=h then lim_(x rarr h)((x+h)f(x)-2hf(h))/(x-h) is equal to

If f(2)=4 and f'(2)=1, then find (lim)_(x rarr2)(xf(2)-2f(x))/(x-2)

LEt f(x) be a differentiable function and f'(4)=5. Then,lim_(x rarr2)(f(4)-f(x^(2)))/(x-2) equals

RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Show that the function f(x)={xsin1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 0\ \ ...

    Text Solution

    |

  2. Discuss the differentiability of f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a ...

    Text Solution

    |

  3. If f(x) is differentiable at x=a , find (lim)(x->a)(x^2f(a)-a^2\ f(x))...

    Text Solution

    |

  4. For what choice of a and b is the function f(x)={x^2\ \ \ ,\ \ \ xlt=c...

    Text Solution

    |

  5. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

    Text Solution

    |

  6. A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all ...

    Text Solution

    |

  7. Show that f(x)=|x-3| is continuous but not differentiable at x=3 .

    Text Solution

    |

  8. Show that f(x)=x^(1//3) is not differentiable at x=0 .

    Text Solution

    |

  9. Show that f(x)={12 x-13 ,\ \ \ if\ xlt=3 2x^2+5,\ \ \ \ \ if\ x >3 is ...

    Text Solution

    |

  10. Show that the function f defined as follows f(x)={3x-2,\ \ \ \ 0<xlt=1...

    Text Solution

    |

  11. Discuss the continuity and differentiability of the function f(x)=|...

    Text Solution

    |

  12. Find whether the following function is differentiable at x = 1 and ...

    Text Solution

    |

  13. Show that the function f(x)={x^msin(1/x), 0 ,\ \ \ x!=0 ,\ \ \ \ \ \...

    Text Solution

    |

  14. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \ ...

    Text Solution

    |

  15. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \ ...

    Text Solution

    |

  16. Find the values of a and b so that the function f(x)={x^2+3x+a ,\ \ if...

    Text Solution

    |

  17. Show that the function f(x)={|2x-3|\ [x],\ \ \ xgeq1sin((pix)/2),\ \ \...

    Text Solution

    |

  18. If f(x)={a x^2-b ,\ \ \ if\ |x|<1 1/(|x|),\ \ \ \ \ \ \ \ \ \ \ \ if\ ...

    Text Solution

    |

  19. Find the values of a and b , if the function f(x) defined by f(x)={x^2...

    Text Solution

    |

  20. If f(x)=x^2+2x+7 , find f\ '\ (3) .

    Text Solution

    |