Home
Class 12
MATHS
if lim(x->0)(ptanqx^2-3cos^2x+4)^(1/(3x^...

if `lim_(x->0)(ptanqx^2-3cos^2x+4)^(1/(3x^2))=e^(5/3)`

A

`p=sqrt2,q= (1)/(2 sqrt2)`

B

`=(1)/(sqrt2), q=2 sqrt2`

C

`p=1,q=2`

D

`p=2,q=4`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|1 Videos

  • LIMIT

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (MATHCHING TYPE PROBLEMS)|1 Videos

  • LIMIT

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|7 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|6 Videos

  • LOGARITHMS

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|19 Videos

Similar Questions

Explore conceptually related problems

If lim_(x rarr0)(p tan qx^(2)-3cos^(2)x+4)^(1/(3x^(2)))=e^(5/3),p,q in R then :

if lim_(x rarr0)(p tan qx^(2)-3cos^(2)x+4)^((1)/(3x^(2)))=e^((5)/(3))

lim_(x->0)(e^(2x)-1)/(3x)

lim_(x rarr0)x^(3)cos(2/x)=

lim_(x rarr0)x^(3)cos(2/x)=

lim_(x->0) (cos2x-cos4x)/(cos3x-cos5x) =

lim_(x-gt0)(cos2x-cos3x)/(cos4x-1)

lim_(x rarr0)((1+5x^(2))/(1+3x^(2)))^(1/x^(2))=

lim_(x rarr0)(cos4x-4cos2x+3)/(x^(4))=

lim_ (x rarr0) (1-cos4x) / ((sin3x) ^ (2))

VIKAS GUPTA (BLACK BOOK)-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. if lim(x->0)(ptanqx^2-3cos^2x+4)^(1/(3x^2))=e^(5/3)

    Text Solution

    |

  2. lim(x->oo) 2(sqrt(25x^2+x)-5x) is:

    Text Solution

    |

  3. Let lim (xtooo) (2 ^(x) +a ^(x) +e ^(x))^(1//x)=L which of the follow...

    Text Solution

    |

  4. Let tan alpha . x + sin alpha · y = alpha and alpha. cosec alpha • x +...

    Text Solution

    |

  5. Let f:R->[-1, 1] be defined as f(x) = cos(sin x), then which of the fo...

    Text Solution

    |

  6. Let f (x) =x + sqrt(x^(2) +2x) and g (x) = sqrt(x^(2) +2x)-x, then:

    Text Solution

    |

  7. Which of the following limits does not exist ?(a) lim(x->oo) cosec^(-1...

    Text Solution

    |

  8. If f(x)=(lim)(nvecoo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) where ...

    Text Solution

    |

  9. Let f:R->R;f(x)={(-1)^n if x=1/(2^(2^n)), n=1,2,3.......... and 0 othe...

    Text Solution

    |

  10. If lim(x->a) f(x) = lim(x->a) [f(x)] ([.] denotes the greatest intege...

    Text Solution

    |

  11. let f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sqrt(2{x}(1-{x})) where {x} deno...

    Text Solution

    |

  12. lim(x->0) (sin(sinx)-sinx)/(ax^3+bx^5+c)=-1/12 then

    Text Solution

    |

  13. If f (x) = lim ( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of...

    Text Solution

    |

  14. lim(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

    Text Solution

    |

  15. If alpha,beta in (-pi/2,0) such that (sin alpha+sinbeta)+(sinalpha)/(s...

    Text Solution

    |

  16. Let f(x)={|x-2|+a^2-6a+9, x < 2 and 5-2x, x >= 2 If lim(x->2) [f(x)] e...

    Text Solution

    |

  17. A circular disk of unit radius is filled with a number of smaller circ...

    Text Solution

    |

  18. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

    Text Solution

    |

  19. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

    Text Solution

    |

  20. A certain function f(x) has the property that f(3x)=alpha f(x) for all...

    Text Solution

    |