Home
Class 12
MATHS
If lim(h rarr 0) (1 + (a)/(x) + (b)/(x^(...

If `lim_(h rarr 0) (1 + (a)/(x) + (b)/(x^(2)))^(2x) = e^(2)`, then the values of a and b, are :

A

`a in R , b = 2`

B

`a = 1, b in R`

C

`a in R, b in R`

D

a =1, b =2

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr 0) (1-ax)^(1/x) =

lim_(x rarr 0) (1+ax)^(b/x)=

If lim_(x rarr 0) ((cos 4x + a cos 2x+b)/(x^(4))) is finite, then the values of a and b are respectively.

lim_(x rarr 0) (1-cos 4x)/(x2) =

lim_(x rarr 0) (sin^(2)(x/4))/(x^(2)) =

lim_(x rarr 0) (e^(x) + e^(-x) -2)/x^(2)=

lim_(x rarr 0) (1-cos (x/3))/(x^(2)) =

lim_(x rarr 0) 2/x log (1+x) =

lim_(x rarr 0) (sin x + log (1-x))/x^(2) =

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The value of lim(x rarr 0) (int(0)^(x^(2))sec^(2)t dt)/(x sin x) is :

    Text Solution

    |

  2. lim(x rarr (pi)/(2)) ((1 - tan x//2)(1-sin x))/((1+tan x//2) (pi - 2x)...

    Text Solution

    |

  3. If lim(h rarr 0) (1 + (a)/(x) + (b)/(x^(2)))^(2x) = e^(2), then the va...

    Text Solution

    |

  4. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0, then ...

    Text Solution

    |

  5. Let a = lim(n rarr oo) (1+2+3+.....+n)/(n^(2))=, b = lim(n rarr oo) (...

    Text Solution

    |

  6. If a,b, c, d are positive, then lim(x rarr oo) (1 + 1/(a+bx))^(c+dx)=

    Text Solution

    |

  7. lim(x rarr 0) (a^(x)-b^(x))/x =

    Text Solution

    |

  8. lim(x rarr 1) (sqrt(x-1) + sqrt(x-1))/(sqrt(x^(2)-1)) =

    Text Solution

    |

  9. lim(x rarr 0) x/(sqrt(x+4)-2) =

    Text Solution

    |

  10. lim(x rarr 0) [[(log(1+x))]/x]=

    Text Solution

    |

  11. lim(x rarr oo)((a^(1/x)+b^(1/x)+c^(1/x))/3)^x, where a, b, c are real ...

    Text Solution

    |

  12. lim(x rarr oo) ((2x+7sinx)/(4x+3cosx)) =

    Text Solution

    |

  13. lim(x rarr 0) (log (1+x))/(3^(x) - 1)=

    Text Solution

    |

  14. lim(theta rarr pi/2) (1-sin theta )/((pi/2 - theta) cos theta)=

    Text Solution

    |

  15. lim(x rarr 0) (x.10^(x)-x)/(1-cos x) =

    Text Solution

    |

  16. lim(x rarr oo) ((x+a)/(x+b))^(x+b) =

    Text Solution

    |

  17. If f(x) = {(2x+b, x lt alpha),(x+d, x gea):} is such that lim(x rarr a...

    Text Solution

    |

  18. The quadratic equation whose roots are l and m, where l = lim(theta ra...

    Text Solution

    |

  19. lim(x rarr 0) (4^(x)-9^(x))/(x*(4^(x)+9^(x)) ) =

    Text Solution

    |

  20. If lim(xtoa)(a^(x)-x^(a))/(x^(x)-a^(a))=-, then :

    Text Solution

    |