Home
Class 12
MATHS
If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2)))...

If `f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2)))` and `phi(x)=cos^(-1)((1-x^(2))/(1+x^(2)))`, then the value of `lim_(x to a) (f(x)-f(a))/(phi(x)-phi(a))(0 lt a lt (1)/(2))` is -

A

`(3)/(2(1+a^(2)))`

B

`-(3)/(2(1+a^(2)))`

C

`(3)/(2)`

D

`-(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 5|80 Videos

  • MAXIMA AND MINIMA

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination E|2 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

Similar Questions

Explore conceptually related problems

If f(x) =cot ^(-1) ((3x -x^(3))/(1-3x^(2))) and g (x) =cos ^(-1) ((1- x ^(2))/(1+x^(2))) then lim _(xtoa) (f(x) -f(a))/(g (x) -g(a)) is equal to-

If f(x)=|(sinx, cosx, tanx),(x^(3),x^(2),x),(2x,1,1)| then the value of lim_(x to 0) (f(x))/(x^(2)) is -

Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1/(sqrt(3))

If phi (x)=f(x)+x f'(x) , then the value of int phi (x) dx is -

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

If lim_(xto0) [1+x+(f(x))/(x)]^(1//x)=e^(3) , then the value of ln(lim_(xto0) [1+(f(x))/(x)]^(1//x)) is _________.

If f(x)= log_3x and phi(x)=x^2 ,then the value of f{varphi(3)} will be

If f(x+3) = 2x^2-3x-1 , find the value of f(x+1).

If phi(x)=lim_(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)) , then

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 7
  1. The value of lim(x to 0) (1-3x)^((3)/(x)) is equal to -

    Text Solution

    |

  2. If y=2sin^(- 1)((x-2)/sqrt(6))-sqrt(2+4x-x^2) then prove that dy/dx at...

    Text Solution

    |

  3. If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) and phi(x)=cos^(-1)((1-x^(2)...

    Text Solution

    |

  4. If y=sec(tan^(-1)x), then (dy)/(dx) is equal to -

    Text Solution

    |

  5. If y=e^(x+e^(x+e^(x+...oo)), then the value of (dy)/(dx) is -

    Text Solution

    |

  6. If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+logsqrt(1-x^(2)), then the value o...

    Text Solution

    |

  7. For |x| lt 1, let y=1+x+x^(2)+…oo, then the value of (dy)/(dx)-y is e...

    Text Solution

    |

  8. Observe the following statements : (i) f(x)=ax^(41)+bx^(-40) rArr (f'...

    Text Solution

    |

  9. If f(y)=e^(y), g(y)=y, y gt 0 and F(t)=int(0)^(t) f(t-y)g(y)dy, then ...

    Text Solution

    |

  10. If m, n in R, then the value of I(m,n)=int(0)^(1) t^(m)(1+t)^(n)dt is...

    Text Solution

    |

  11. The value of int(-2)^(2)[p log((1+x)/(1-x))+q log ((1-x)/(1+x))^(-2)+...

    Text Solution

    |

  12. The value of int (f'(x))/(f(x)log{f(x)})dx is equal to -

    Text Solution

    |

  13. The value of int e^(-logx)dx is -

    Text Solution

    |

  14. If f(x)=(e^(x))/(1+e^(x)),I(1)=int(f(-a))^(f(a))xg{x(1-x)}dx and I(2)...

    Text Solution

    |

  15. The value of int sqrt(x)e^(sqrt(x))dx is -

    Text Solution

    |

  16. The value of int(-1)^(1)|1-x| dx is equal to -

    Text Solution

    |

  17. The value of int(0)^((pi)/(8))cos^(3)4 theta d theta is equal to -

    Text Solution

    |

  18. The value of int(dx)/(sin x cos x) is equal to -

    Text Solution

    |

  19. If int (e^(x)(1+sinx))/(1+cos x)dx=e^(x)f(x)+c, then the value of f(x...

    Text Solution

    |

  20. The value of int(0)^(pi) (cosx dx)/(x^(4)+(pi-x)^(4)) is equal to -

    Text Solution

    |