Home
Class 12
MATHS
Let f:R toR be such that f(1)=3 and f(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

A

1

B

`e^(1//2)`

C

`e^(2)`

D

`e^(3)`.

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise MCQs (LEVEL-II)|35 Videos

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise Latest Question from AIEEE/JEE Examinations|7 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise Recent competitive Questions|12 Videos

Similar Questions

Explore conceptually related problems

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

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

If f(x) is a quadratic polynomial such that f(0) = 2, f(0) = -3 and f'(0) = 4 , then int_(-1)^(1) f(x) dx equals:

Let f(x) be differntiable on the interval (0,oo) such that f(1)=1 and lim_(t tox)(t^(2)f(x)-x^(2)f(t))/(t-x)=1 for each xgt0 . Then f(x) is :

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 :

Let f:R to R be a positive increasing function with lim_(x to oo) (f(3x))/(f(x))=1 . Then lim_(x to oo) (f(2x))/(f(x))=

Let f(x), g(x) be differentiable functions and f(1) = g(1) = 2, then : lim_(x rarr 1) (f(1) g(x) - f(x) g(1) - f(1) + g(1))/(g(x) - f(x)) equals :

Let, f : R rarr R be given by f(x) = tan x . Then f^-1(1) =

Let f(x) be a polynomial of degree four having extreme values at x = 1 and x = 2. If lim_(x to 0) [1+(f(x))/(x^(2))]=3 , then f(2) is equal to :

Let f:(-1,1)toR be a differentiable function with f(0)=-1 and f'(0)=1 . Let g(x)=[f(2f(x)+2)]^(2) . Then g'(0)=

MODERN PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -RCQs (Questions from Karnataka CET & COMED)
  1. Let f:R toR be such that f(1)=3 and f(1)=6. Then lim(xto0)(f(1+x)/(f(1...

    Text Solution

    |

  2. If the three function f(x),g(x) and h(x) are such that h(x)=f(x)g(x) a...

    Text Solution

    |

  3. The drivative of e^(ax)cos bx with rexpect to x is re^(ax)cosbx+"tan"^...

    Text Solution

    |

  4. If x=acos^(3)theta and y=asin^(3)theta, then (dy)/(dx)=

    Text Solution

    |

  5. If y=tan^(-1)sqrt(x^(2)-1), then the ratio (d^(2)y)/(dx^(2)):(dy)/(dx)...

    Text Solution

    |

  6. If sqrt(r ) =ae^(thetacotalpha) where a and alpha are real numbers the...

    Text Solution

    |

  7. The derivative of "tan"^(-1)(sinx)/(1+cosx) w.r.t. "tan"^(-1)(cosx)/(1...

    Text Solution

    |

  8. d/(dx)[cos^(2)(cot^(-1)sqrt((2+x)/(2-x)))]

    Text Solution

    |

  9. If f(x)=((sin^(2)x)/(1+cotx))+(cos^(2)x)/(1+tan), then f'((pi)/(4)) is...

    Text Solution

    |

  10. If cos^(-1)((y)/(b))=nlog((x)/(n)), then :

    Text Solution

    |

  11. f(x)=2a-x in -altxlta=3x-2a in a lex. Then which of the following i...

    Text Solution

    |

  12. If x+y=tan^(-1)y" and "(d^(2)y)/(dx^(2))=f(y)(dy)/(dx), then f(y)=

    Text Solution

    |

  13. Let f(x) = cos^(-1) [(1)/(sqrt13) (2 cos x - 3 sin x)]. Then f(0.5) =

    Text Solution

    |

  14. If y=(1+x)(1+x^(2))(1+x^(4)), then (dy)/(dx) at x=1 is :

    Text Solution

    |

  15. If y = (tan^(-1)x)^(2) then show that (x^(2) + 1)^(2) (d^2 y)/(dx^2) +...

    Text Solution

    |

  16. If the function f(x) defined by f(x)=(x^(100))/(100)+(x^(99))/(99)+....

    Text Solution

    |

  17. Which of the following functions is differentiable at x=0. ?

    Text Solution

    |

  18. If x=a(cost+logtant//2),y=asint, then (dy)/(dx)=

    Text Solution

    |

  19. If f(x)=xtan^(-1)x, then lim(xto1)(f(x)-f(1))/(x-1)=

    Text Solution

    |

  20. If f(y)=f(x^(2)+2) and f'(3)=5, then (dy)/(dx) at x=1 is :

    Text Solution

    |

  21. If x = a cos^(3) theta , y = a sin^(3) theta , then 1+((dy)/(dx))^(2)...

    Text Solution

    |