Home
Class 12
MATHS
Let f:RtoR be such that f(1)=3 andf'(1)=...

Let `f:RtoR` be such that `f(1)=3` and`f'(1)=6`. Then `lim_(xto0)[(f(1+x))/(f(1))]^(1//x)` equals

A

1

B

`e^(1/2)`

C

`e^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    ARIHANT MATHS|Exercise Exercise For Session 1|9 Videos

  • LIMITS

    ARIHANT MATHS|Exercise Exercise For Session 2|5 Videos

  • LIMITS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|27 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|4 Videos

Similar Questions

Explore conceptually related problems

Let f : R to R be such that f (1) = 3 and f'(1) = 6. Then, lim_( x to 0) [(f(1+x))/(f(1))]^(1//x) equals

f:RtoR such that f(2)=5 and f'(2)=10 then lim_(xto0) ((f(2+x))/(f(2)))^(1//x) is equal to:

A function f:R rarr R is such that f(1)=3 and f'(1)=6. Then lim_(x rarr0)[(f(1+x))/(f(1))]^(1/x)=

Let f:R rarr R be such that f(1)=3andf'(1)=6. Then lim_(x rarr0)((f(1+x))/(f(1)))^(1/x)=(a)1( b) e^((1)/(2))(c)e^(2) (d) e^(3)

Let f:RrarrR be such that f(a)=1, f(a)=2 . Then lim_(x to 0)((f^(2)(a+x))/(f(a)))^(1//x) is

Let R rarr R be such that f(1)=3 and *f'(1)=6. then lim_(x rarr0)((f(1+x))/(f(1))) equal : (1)1(2)e^((1)/(2))(3)e^(2) (4) e^(3)

If f(1)=3 and f'(1)=6 , then lim_(x rarr0)(sqrt(1-x)))/(f(1))

If f'(x)=f(x) and f(0)=1 then lim_(x rarr0)(f(x)-1)/(x)=

ARIHANT MATHS-LIMITS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let alpha, beta in R such that lim(x ->0) (x^2sin(betax))/(alphax-sin...

    Text Solution

    |

  2. Let m and n be two positive integers greater than 1.If lim(alpha->0) (...

    Text Solution

    |

  3. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

    Text Solution

    |

  4. The largets value of non negative integer for which lim(x->1){(-a x+si...

    Text Solution

    |

  5. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

    Text Solution

    |

  6. The lim(xto(pi)/2)(cot x-cosx)/((pi-2x)^(3)) equals

    Text Solution

    |

  7. Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

    Text Solution

    |

  8. lim(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to

    Text Solution

    |

  9. lim(xto0)(sin(picos^(2)x))/(x^(2)) is equal to

    Text Solution

    |

  10. lim(xto0)((1-cosx)(3+cosx))/(x tan 4x) is equal to

    Text Solution

    |

  11. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  12. let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

    Text Solution

    |

  13. If ("lim")(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in ...

    Text Solution

    |

  14. For xgt0, lim(xto0) {(sinx)^(1//x)+((1)/(x))^sinx}, is

    Text Solution

    |

  15. underset(h to 0)lim (f(2h+2+h^(2)))/(f(h-h^(2)+1)-f(1))"given that "f'...

    Text Solution

    |

  16. lim(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0, when n is a non-zero posit...

    Text Solution

    |

  17. The integer n for which lim(x rarr 0) ((cos x-1) ( cos x - e^x))/x^n i...

    Text Solution

    |

  18. Let f:RtoR be such that f(1)=3 andf'(1)=6. Then lim(xto0)[(f(1+x))/(f(...

    Text Solution

    |

  19. For x epsilonR, lim(xto oo)((x-3)/(x+2))^(x) is equal to

    Text Solution

    |