Home
Class 12
MATHS
Let f(2)=4 and f'(2)=4. Then lim(xto2)...

Let `f(2)=4` and `f'(2)=4`.
Then `lim_(xto2)(xf(2)-2f(x))/(x-2)` is given by :

A

2

B

(-2)

C

(-4)

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
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)

Evaluate lim_(xto2)(x^(3)-2^(3))/(x-2)

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

If f(x)=xtan^(-1)x , then lim_(xto1)(f(x)-f(1))/(x-1)=

Let F : R to R be a differentiable function having : f(2) = 6, f'(2) = 1/48 Then lim_(x to 2) int_(6)^(f(x)) (4 t^3)/(x-2) dt equals :

lim _( xto 2) (x^(2) + 4) /( x+1 )

Let f:R toR be such that f(1)=3 and f(1)=6 . Then lim_(xto0)(f(1+x)/(f(1)))^(1//x) equal

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

Let f(x)=x^4-x^3 then find f '(2)

If f(a)=2,f'(a)=1,g(a)=-,g'(a)=2 , then the value of lim_(xtoa)(g(x)f(a)-g(a)f(x))/(x-a) is :

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The value of lim(x rarr 0) (int(0)^(x^(2))cos t^(2)dt)/(x sin x) is :

    Text Solution

    |

  2. lim(x rarr 0) (sin nx[(a-n)nx - tan x])/(x^(2)) = 0, where n is non-ze...

    Text Solution

    |

  3. Let f(2)=4 and f'(2)=4. Then lim(xto2)(xf(2)-2f(x))/(x-2) is given b...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |