Home
Class 11
MATHS
Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+...

Let `f(x)=(lim)_(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot` Then `f(pi/2)` equal to (a)0 (b) equal to 1 (c)In `pi/2` (d) non-existent

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x)

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to pi/2 (b) -pi (c) pi (d) -pi/2

("lim")_(ntooo)1/(1+nsin^2n x) is equal to (a) -1 (b) 0 (c) 1 (d) oo

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these

int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logx dx is equal to (a) -pi/2logpi (b) 0 (c) pi/2log2 (d) none of these

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to (a) 0 (b) 2pi (c) pi (d) none of these

If f(n)=lim_(xto0) {(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"sin"(x)/(2^(n)))}^((1)/(x)) then find lim_(ntooo) f(n).

If lim_(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to 4 (b) 1 (c) 2 (d) 3

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to 1 (b) 2 (c) 1/2 (d) none of these

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) ...

    Text Solution

    |

  2. If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

    Text Solution

    |

  3. Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...

    Text Solution

    |

  4. If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

    Text Solution

    |

  5. A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...

    Text Solution

    |

  6. If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...

    Text Solution

    |

  7. If x=logp and y=1/p ,then (a)(d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2...

    Text Solution

    |

  8. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)...

    Text Solution

    |

  9. Let y=ln(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

    Text Solution

    |

  10. Find (dy)/(dx)"for"y=xsinxlogxdot

    Text Solution

    |

  11. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

    Text Solution

    |

  12. Differentiate y=(e^x)/(1+sinx)

    Text Solution

    |

  13. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

    Text Solution

    |

  14. lf y=sqrt((1-x)/(1+x)) find dy/dxand prove that (1-x^2)(dy)/(dx)+y=0

    Text Solution

    |

  15. If g(x)=(f(x))/((x-a)(x-b)(x-c)),where f(x) is a polynomial of degree ...

    Text Solution

    |

  16. If f(x) = cosx. cos2x. Cos4x. Cos8x.cos16x, then f '(pi/4) is :

    Text Solution

    |

  17. f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,Pn be th...

    Text Solution

    |

  18. If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...

    Text Solution

    |

  19. If d/(dx)[(x^m-A1x^(m-1)+A2x^(m-2)-.......+(-1)^m Am)e^x]=x^m e^x , f...

    Text Solution

    |

  20. If y=|[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1, 1]| find (dy)/(dx)dot

    Text Solution

    |