Home
Class 12
MATHS
(lim)(xvec0^+)1/(xsqrt(x))("a t a n"^(-1...

`(lim)_(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x))/b)` has the value equal to `(a-b)/3` b. 0 c. `((a^2-b^2))/(6a^2b^2)` d.`` `(a^2-b^2)/(3a^2b^2)`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

lim_(x rarr0^(+))(1)/(x sqrt(x))(atan^(-1)(sqrt(x))/(a)-b tan^(-1)(sqrt(x))/(b)) has the value equal to (a-b)/(3) b.0 c.((a^(2)-b^(2)))/(6a^(2)b^(2)) d.(a^(2)-b^(2))/(3a^(2)b^(2))

(lim)_(xvec0)((sqrt(1+x s in x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/6 b. 6 c.3 d. 2

The value of the limit ("lim")_(xvec0)(a^(sqrt(x))-a^(1sqrt(x)))/(a^(sqrt(x))+a^(1sqrt(x))),a >1,i s 4 (b) 2 (c) -1 (d) 0

If int_(0)^(b)(1)/(sqrt(1+x)-sqrt(x))dx=(2)/(3)(2sqrt(2)) , then b =

If x=root(3)(7+5sqrt(2))-(1)/(root(3)(7+5sqrt(2))), then the value of x^(3)+3x-14 is equal to 1 b.0 c.2 d.4

If x=root(3)(7+5sqrt(2))-(1)/(root(3)(7+5sqrt(2))), then the value of x^(3)+3x-14 is equal to 1(b)0(c)2 (d) 4

(lim_(x rarr0)(sqrt(1+x)-1)/(x) is equal to a.1b.0 c.2d.(1)/(2)

int_(0)^((pi)/(3))(tan x)/(sqrt(2k sec x))dx=1-(1)/(sqrt(2)), then value of k is (a) 2 (b) 1 (b) 1 (d) (1)/(4)

If A=tan^(-1)((x sqrt(3))/(2k-x)) and B=tan^(-1)((2x-k)/(k sqrt(3))) then find the value of A-B(A)0^(@)(B)30^(@)(C)60^(@)(D)45^(@)

lim_(x rarr0)(sin^(2)x)/(sqrt(2)-sqrt(1+cos x))=(A)sqrt(2)(B)2(C)

BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. Let f(x)=|cosxsinxcosxcos2xsin2x2cos2xcos3xsin3x3cos3x| then f'(pi/2)=...

    Text Solution

    |

  2. people living at Mars ,instead of the usual definition of derivative D...

    Text Solution

    |

  3. (lim)(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x)...

    Text Solution

    |

  4. Let y=ln(1+cosx)^2 then the value of (d^2y)/(dx^2)+2/(e^(y//2)) equals...

    Text Solution

    |

  5. If a curve is represented parametrically by the equation x=f(t) and y=...

    Text Solution

    |

  6. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  7. The derivative of the function, f(x)=cos^(-1){(1)/(sqrt13)(2cosx-3sin...

    Text Solution

    |

  8. Left hand derivative of sin^(- 1)((2x)/(1+x^2)) with respect to cos^-...

    Text Solution

    |

  9. If x^2+y^2=R^2(w h e r eR >0)a n dk=(y^n)/((1+y^2)^3) then find k in ...

    Text Solution

    |

  10. If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p))...

    Text Solution

    |

  11. A curve is represented parametrically by the equations x = e^t cos t a...

    Text Solution

    |

  12. If F(t)=int(x+y)dt then the value of F(pi/2)-F(0) is 1 (b) -1 (...

    Text Solution

    |

  13. If 2^x+2^y=2^(x+y) then (dy)/(dx)

    Text Solution

    |

  14. Two functions f & g have first & second derivatives at x=0 & satisfy t...

    Text Solution

    |

  15. Let P(x) be the polynomial x^3+a x^2+b x+c , where a ,\ b ,\ c in R ....

    Text Solution

    |

  16. If sqrt(y+x)+sqrt(y-x)=c (where c!=0 ), then dy/dx

    Text Solution

    |

  17. For the function y=f(x)=(x^2+b x+c)e^x , which of the following holds?...

    Text Solution

    |

  18. Let f'(x)=3x^2sin1/x-xcos1/x , if x!=0\ ; f(0)=0 and f(1//pi)=0 then: ...

    Text Solution

    |

  19. If f(x)=xdot|x|, then its derivative is : (a)2x (b) -2x (c) 2|x|...

    Text Solution

    |

  20. Find derivative of u(x) u( x )= [ ln( 1+ sin2x ), if x>0 ...

    Text Solution

    |