Home
Class 12
MATHS
If lim(x rarr 0) (1 + px)^(q/x) = e^(4),...

If `lim_(x rarr 0) (1 + px)^(q/x) = e^(4), where `p,q in N`, then

A

p =4,q=2

B

p = 8, q=4

C

p = 16, q = 8

D

p = 4, q = 1

Text Solution

Verified by Experts

The correct Answer is:
D
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)=

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

lim_(x rarr 0) (a^(x)-b^(x))/x =

lim_(x rarr 0) (sin(4x)/(5x) )=

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

lim_(x rarr 0) ((1+x)^(n)-1)/x is

lim_(x rarr 0) (sin x^(o) )/x=

lim_(x rarr 0) (sqrt(1+x)-1)/x =

lim_(x rarr 0) (|sin x|)/x is

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. lim(x rarr 0) [(10^(x)-2^(x)-5^(x)+1)/(x . tan x)] =

    Text Solution

    |

  2. lim(n rarr oo) (3.2^(n+1) - 4.5^(n+1))/(5.2^(n) + 7.5^(n)) =

    Text Solution

    |

  3. If lim(x rarr 0) (1 + px)^(q/x) = e^(4), where p,q in N, then

    Text Solution

    |

  4. lim(x rarr 0) (sin x + log (1-x))/x^(2) =

    Text Solution

    |

  5. Let f(x) = {(1+x, x gt 0),(x, x le 0):} . Lim(x rarr 0) f(x) =

    Text Solution

    |

  6. lim(h rarr 0) (sqrt(x+h) - sqrtx)/h =

    Text Solution

    |

  7. The values of a and b so that lim(x rarr oo) [(x^(2)+1)/(x+1) - ax-b] ...

    Text Solution

    |

  8. lim(x rarr 2) (sqrt(x-2) + sqrtx - sqrt2)/(sqrt(x^(2)-4)) =

    Text Solution

    |

  9. lim(x rarr pi//3) (2 sin (x-pi//3))/(1-2 cos x) equals :

    Text Solution

    |

  10. Let f(x) = 4x^(9)-3x^(8)+2x^(7)+x^(3)+x^(2)-4, then lim(h rarr 0) (f(1...

    Text Solution

    |

  11. Let f(x) = {{:(x (sin 1//x + sin (1//x^(2))),,x ne 0),(0,,x = 0):} The...

    Text Solution

    |

  12. If lim(x rarr -a) (x^(9)+a^(9))/(x+a) = 9, then a =

    Text Solution

    |

  13. lim(x rarr oo) [sqrt(x+sqrt(x + sqrt (x-)) sqrtx]=

    Text Solution

    |

  14. lim(x rarr 1) (log(e)x)/(x-1) equals :

    Text Solution

    |

  15. If f be a function such that f(9) = 9 and f'(9) = 3, then : lim(x ra...

    Text Solution

    |

  16. lim(x rarr 0) ((1^(x)+2^(x)+3^(x)+……….+n^(x))/n)^(1/x) =

    Text Solution

    |

  17. If f(x) = (sin (e^(x-2) - 1))/(log (x - 1)), then lim(x rarr 2) f(x) i...

    Text Solution

    |

  18. lim(x rarr 0) ((tan x -x)/x). (Sin) 1/x =

    Text Solution

    |

  19. If lim(x rarr 0) (x(1+m cos x)-n(sin x))/x^(3) =1 then

    Text Solution

    |

  20. lim(x rarr 0) (cos x + a sin bx)^(1/x) =

    Text Solution

    |