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

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMIT AND CONTINUITY

    MODERN PUBLICATION|Exercise LATEST QUESTIONS FROM AIEEE/JEE EXAMINATIONS|11 Videos

  • LIMIT AND CONTINUITY

    MODERN PUBLICATION|Exercise QUESTIONS FROM KARNATAKA CET & COMED|7 Videos

  • LIMIT AND CONTINUITY

    MODERN PUBLICATION|Exercise QUESTIONS FROM KARNATAKA CET & COMED|7 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise QUESTION FROM KARNATAKA CET & COMED|10 Videos

  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise QUESTIONS FROM KARNATAKA CET & COMED|9 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) (sin x^(o) )/x=

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

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) (sqrt(1+x)-1)/x =

MODERN PUBLICATION-LIMIT AND CONTINUITY -MULTIPLE CHOICE QUESTIONS(LEVEL - II )
  1. Let f(x) = {{:(x (sin 1//x + sin (1//x^(2))),,x ne 0),(0,,x = 0):} The...

    Text Solution

    |

  2. lim(x rarr 0) (tan [e^(2)]x^(2)-tan[-e^(2)]x^(2))/(sin^(2)x) equals :

    Text Solution

    |

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

    Text Solution

    |

  4. Let f(x) = 3x^(10) - 7x^(8) + 5x^(6) - 21x^(3) + 3x^(2) - 7. Then lim(...

    Text Solution

    |

  5. Let f(x) = lt x gt^("*"), where lt x gt^("*") is the distance from x t...

    Text Solution

    |

  6. lim(x rarr 2^(+)) (([x]^(3))/(3) - [(x)/(3)]^(3)) equals :

    Text Solution

    |

  7. If the function f(x) = [((cos x)^(1//x),x ne 0),(k,x = 0):} is continu...

    Text Solution

    |

  8. Let f(x) = |x| "cos" (1)/(x) + 15x^(2), x ne 0, = k, x = 0, then f(x...

    Text Solution

    |

  9. If lim(x rarr a^(+)) f(x) = l = lim(x rarr a^(-)) g(x) and lim(x rarr ...

    Text Solution

    |

  10. The following are continuous on (0, pi) :

    Text Solution

    |

  11. The value of b for which the function : f(x) = {{:(5x-4,"if",0lt x le ...

    Text Solution

    |

  12. Let f(x) = [{:(5^(1//x),x lt 0),(lambda[x],x le 0","lambda in R):}, th...

    Text Solution

    |

  13. Let f(x) = [{:((g(x) - g(a))/(x-a),x ne 0),(g'(a),x = a):}, where g is...

    Text Solution

    |

  14. Let f(x) = {{:(1,x le -1),(|x|,-1 lt x lt 1),(0,x ge 1):}, then :

    Text Solution

    |

  15. The function f(x) = [x] is :

    Text Solution

    |

  16. Let f(x) = (1 - cos px)/(x sin x), where x ne 0 and f(0) = (1)/(2). If...

    Text Solution

    |

  17. Let f(x) = (1-sin x)/((pi - 2x)^(2)),"where x" ne pi//2 and f(pi//2) =...

    Text Solution

    |

  18. Let f(x) = (tan (pi//4-x))/(cot 2x)"for x" ne pi//4, then for f to be ...

    Text Solution

    |

  19. Let f(x) = [{:((x^(2))/(a),0 le x lt 1),(a,1 le x lt sqrt(2)),((2b^(2)...

    Text Solution

    |

  20. The value of f(0) so that the function : f(x) = (sqrt(1 + x) - (1+x)^(...

    Text Solution

    |