Home
Class 12
MATHS
If f(x) is derivable at x=2 such that f ...

If `f(x)` is derivable at `x=2` such that `f (2)=2 and f'(2)=4,` then the value of `lim _(h to 0)(1)/(h ^(2)) (ln (f (2+ h ^(2)))-ln (f(2-h^(2))))` is equal to:

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|36 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|30 Videos
  • COMPOUND ANGLES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

If f(x) is derivable at x=2 such that f(2)=2 and f'(2)=4 , then the value of lim_(h rarr0)(1)/(h^(2))(ln f(2+h^(2))-ln f(2-h^(2))) is equal to

If f(x) is derivable at x=3 and f'(3)=2 , then value of lim_(hto0)(f(3+h^(2))-f(3-h^(2)))/(2h^(2)) is less than

The value of lim_(hto0) (In (1+2h)-2ln (1+h))/(h^2) , is

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

If f(x) is derivable at x=5, f'(5)=4 , then evaluate lim_(hto0)(f(5+h^(3))-f(5-h^(3)))/(2h^(3)

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

If f(x) = log_(e) ((1-x)/(1+x)) , then f((2x)/(1 + x^(2))) is equal to :

If f(x) is the antidervative of (1+2 tanx(tanx+secx))^((1)/(2)) and f((pi)/(6))=log2 , then the value of f(0) is

If log_(4)((2f(x))/(1-f(x)))=x, " then "(f(2010)+f(-2009)) is equal to

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

VIKAS GUPTA (BLACK BOOK) ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f(x) is derivable at x=2 such that f (2)=2 and f'(2)=4, then the va...

    Text Solution

    |

  2. Let f (x)= {{:(ax (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...

    Text Solution

    |

  3. If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...

    Text Solution

    |

  4. If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(3)), where k ...

    Text Solution

    |

  5. The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix)...

    Text Solution

    |

  6. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  7. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  8. Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim( n to oo) (f...

    Text Solution

    |

  9. Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...

    Text Solution

    |

  10. If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable...

    Text Solution

    |

  11. Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...

    Text Solution

    |

  12. If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...

    Text Solution

    |

  13. f (x) =a cos (pix)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...

    Text Solution

    |

  14. Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...

    Text Solution

    |

  15. Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...

    Text Solution

    |

  16. If y=e^(2 sin ^(-1)x) then |((x ^(2) -1) y ^('') +xy')/(y)| is equal t...

    Text Solution

    |

  17. Let f be continuous function on [0,oo) such that lim (x to oo) (f(x)+ ...

    Text Solution

    |

  18. Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...

    Text Solution

    |

  19. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  20. Let f :R to R be a differentiable function satisfying: f (xy) =(f(x)...

    Text Solution

    |

  21. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

    Text Solution

    |