Home
Class 12
MATHS
If f(2)=4 and f^(prime)(2)=1 , then find...

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

A

2

B

4

C

`-2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`underset(x to 2)lim (xf(2)-2f(x))/(x-2)`
`underset(x to 2)lim (xf(2)-2f(2)+2f(2)-2f(x))/(x-2)`
`underset(x to 2)lim (xf(2)-2f(2)+2f(2)-2f(x))/(x-2)`
`underset(x to 2)lim ((x-2)f(2))/(x-2)-2 underset(x to 2)lim (f(x)-f(2))/(x-2)`
`=f(2)-2f'(2) [therefore f'(2)=underset(x to 2)lim (f(x)-f(2))/(x-2)]`
`=4-2xx1=2 [therefore f(2)=4 and f'(2)=1]`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|143 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

Similar Questions

Explore conceptually related problems

If f(2)=2a n df^(prime)(2)=1, then find (lim)_(xvec2)(xf(2)-2f(x))/(x-2)

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

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

If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a) is (a) -5 (b) 1/5 (c) 5 (d) none of these

If f'(2)=2, f''(2) =1 , then lim_(xrarr2)(2x^2-4f'(x))/(x-2) , is

If f(1)=1,f^(prime)(1)=2, then write the value of lim_(x->1)(sqrt(f(x))-1)/(sqrt(x)-1)

If f'(x)=x/2 + 2/x and f(1)=5/4 , then find f(x) .

If f(x)=x^(2)-4 then find f'(2).

If y=f((2x-1)/(x^2+1)) and f^(prime)(x)=sinx^2 , find (dy)/(dx) .

If f^(prime)(x)=8x^3-2x ,f(2)=8, find f(x)

OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

    Text Solution

    |

  2. The function f(x) = (4-x^(2))/(4x-x^(3)) is discontinuous at

    Text Solution

    |

  3. Let f(x)=|x| and g(x)=|x^3| , then (a).f(x) and g(x) both are continuo...

    Text Solution

    |

  4. The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuou...

    Text Solution

    |

  5. The set of points where the function f(x)=x|x| is differentiable is...

    Text Solution

    |

  6. On the interval I = [-2, 2], if the function f(x) = {{:((x+1)e^(-((1)/...

    Text Solution

    |

  7. If f(x)={{:(,(|x+2|)/(tan^(-1)(x+2)),x ne -2),(,2, x=-2):}, then f(x) ...

    Text Solution

    |

  8. Let f(x)=(x+|x|)|x| . Then, for all x f is continuous

    Text Solution

    |

  9. The set of all points where the function f(x)=sqrt(1-e^(-x^2)) is di...

    Text Solution

    |

  10. The function f(x)=e^(-|x|) is continuous everywhere but not differe...

    Text Solution

    |

  11. The function f(x)=[cos x] is

    Text Solution

    |

  12. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] ...

    Text Solution

    |

  13. If f(x) = sin ^(-1)((2x)/(1 + x^(2))) then f (x) is differentiable in ...

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then f...

    Text Solution

    |

  16. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)...

    Text Solution

    |

  17. If f(x)= | log10x| then at x=1.

    Text Solution

    |

  18. If f(x)=|log(e) x|,then

    Text Solution

    |

  19. If f(x)=|log(e)|x||," then "f'(x) equals

    Text Solution

    |

  20. Let f(x)={1/(|x|)\ \ \ \ \ for\ |x|geq1a x^2+b\ \ \ \ \ \ \ \ for\ |x|...

    Text Solution

    |

  21. Let h(x)="min "{x,x^(2)} for every real number of x. Then, which one o...

    Text Solution

    |