Home
Class 12
MATHS
Let f:RrarrR be such that f(a)=1, f(a)=2...

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

A

`e^(2)`

B

`e^(4)`

C

`e^(-4)`

D

`1//e`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xrarr0)(lim)((f^(2)(a+x))/(f(a)))^(1//x)`
`" "=e^(underset(xrarr0)(lim)((f^(2)(a+x)-f(a))/(xf(a))))`
`" "=e^(underset(xrarr0)(lim)(f^(2)(a+x)-(f(a))^(2))/(x))`
`" "=e^(underset(xrarr0)(lim)((f(a+x)-f(a))(f(a+x)+f(a)))/(x))`
`" "=e^(underset(xrarr0)(lim)2f(a)((f(a+x)-f(a)))/(x))`
`" "=e^(underset(xrarr0)(lim)2f(a)f'(a))`
`" "=e^(4)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Multiple Correct Answers Type|4 Videos

  • LIMITS

    CENGAGE|Exercise ComprehensionType|2 Videos

  • LIMITS

    CENGAGE|Exercise JEE Advanced Previous Year|7 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Let f: R->R be such that f(1)=3a n df^(prime)(1)=6. Then lim_(x->0)((f(1+x))/(f(1)))^(1//x)= (a) 1 (b) e^(1/2) (c) e^2 (d) e^3

If f(1)=1 and f'(1)=2 then lim_(xto1)((f(x))^(2)-1)/(x^(2)-1) is

f(x)=sqrt(x^(2)+1) then lim_(xto3)(f(x)-sqrt(10))/(x-3) is

Let f :RtoR be a positive, increasing function with lim_(xtooo) (f(3x))/(f(x))=1 . Then lim_(xtooo) (f(2x))/(f(x)) is equal to

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x)

Let f: RrarrR, where f(x)=sinx , Show that f is into.

Let f(x) be the fourth degree polynomial such that f^(prime)(0)=-6,f(0)=2 and (lim)_(x->1)(f(x))/((x-1)^2)=1 The value of f(2) is a. 3 b. 1 c. 0 d. 2

Let a_1,a_2…….a_n be fixed real number such that f(x)=(x-a_1)(x-a_2)……….(x-a_n) what lim_(x to a) f(x) For a ne a_1,a_2……a_n compute lim_(x to 0) f(x)

CENGAGE-LIMITS-Single Correct Answer Type
  1. If agt0, b gt0 than lim(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=

    Text Solution

    |

  2. If f(x)=lim(nrarroo) (cos(x)/(sqrtn))^(n), then the value of lim(xrarr...

    Text Solution

    |

  3. lim(xrarr0) (log(x^(x^(2))+2sqrtx))/(tansqrtx) is equal to

    Text Solution

    |

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

    Text Solution

    |

  5. The value of lim(nrarroo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1) is

    Text Solution

    |

  6. If f(n)=("lim")(xvec0)"{"(1+s in x/2)(1+s in x/(x^2))(1+s in x/(x^n))"...

    Text Solution

    |

  7. lim(nrarroo) (1-x+x.root n e)^(n) is equal to

    Text Solution

    |

  8. underset(xrarr1)(lim)(root(13)x-root7x)/(root5x-root3x) is

    Text Solution

    |

  9. lim(xrarr1) (root(13)x-root7x)/(root5x-root3x) is

    Text Solution

    |

  10. The value of lim(x rarr 0) (1-cos2x)/(e^(x^(2))-e^(x)+x) is

    Text Solution

    |

  11. If f(a)=(1)/(4), then lim(hrarr0) (f(a+2h^(2))-f(a-2h^(2)))/(f(a+h^(3)...

    Text Solution

    |

  12. (lim)(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x)...

    Text Solution

    |

  13. The value of lim(xrarr0) ((1+2x)/(1+3x))^((1)/(x^(2))).e^((1)/(e^(x)))...

    Text Solution

    |

  14. If F:R rarr R be a differentiable function at x = 0 satisfying f(0)=0 ...

    Text Solution

    |

  15. The value of lim(xrarr(3pi)/(4)) (1+root3(tanx))/(1-2cos^(2)x) is

    Text Solution

    |

  16. Let g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2 m and n integers, m ne0...

    Text Solution

    |

  17. Number of integral values of lambda for which lim(xrarr1) sec^(-1)((la...

    Text Solution

    |

  18. If lim(xrarr0) (e^(ax)-e^(x)-x)/(x^(2))=b (finite), then

    Text Solution

    |

  19. If lim(xrarr0)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0, then a+b is equal to

    Text Solution

    |

  20. If lim(xrarroo) xlog(e)(|(alpha//x,1,gamma),(0,1//x,beta),(1,0,1//x)|)...

    Text Solution

    |