Home
Class 12
MATHS
If f(2)=2 and f^(prime)(2)=1, then find ...

If `f(2)=2 and f^(prime)(2)=1,` then find `(lim)_(x->2)(xf(2)-2f(x))/(x-2)`

Text Solution

AI Generated Solution

To solve the limit problem given \( f(2) = 2 \) and \( f'(2) = 1 \), we need to evaluate: \[ \lim_{x \to 2} \frac{xf(2) - 2f(x)}{x - 2} \] ### Step 1: Substitute the known value of \( f(2) \) ...
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(2)=4 and f'(2)=1, then find (lim)_(x rarr2)(xf(2)-2f(x))/(x-2)

lim_(x rarr2)(f(x)-f(2))/(x-2)=

if f(2)=4,f'(2)=1 then lim_(x rarr2)(xf(2)-2f(x))/(x-2)

if f(2)=4,f'(2)=1 then lim_(x rarr2)(xf(2)-2f(x))/(x-2)

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

If f(x) is differentiable at x=a and f^(prime)(a)=1/4dot Find (lim)_(h->0)(f(a+2h^2)-f(a-2h^2))/(h^2)

Let f(2)=4 and f'(2)=4. Then lim_(x rarr2)(xf(2)-2f(x))/(x-2) is equal to

Let f (2) = 4 and f '(2) =4. If lim _( xto 2) (xf (2) -2 f (x))/(x-2)=-a, then a is

RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Discuss the differentiability of f(x)=x|x| at x=0

    Text Solution

    |

  2. Show that the function f(x)={ x^2sin(1/x) , when x!=0 and 0 when x=0 }...

    Text Solution

    |

  3. If f(2)=2 and f^(prime)(2)=1, then find (lim)(x->2)(xf(2)-2f(x))/(x-2)

    Text Solution

    |

  4. A function f:R -> R satisfies the equation f(x+y)=f(x)f(y) for all x,y...

    Text Solution

    |

  5. Show that f(x)=|x| is not differentiable at x=0 .

    Text Solution

    |

  6. Show that the function f(x)={x-1\ \ \ ,\ \ \ if\ x<2 2x-3\ \ \ ,\ \ \ ...

    Text Solution

    |

  7. Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is dif...

    Text Solution

    |

  8. Show that f(x)=x^2 is differentiable at x=1 and find f^(prime)(1) .

    Text Solution

    |

  9. Show that the function f(x)=|x+1|+|x-1| for all x in R , is not diffe...

    Text Solution

    |

  10. Discuss the differentiability of f(x)=x|x| at x=0 .

    Text Solution

    |

  11. Show that the function f(x)={xsin1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 0\ \ ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |