Home
Class 12
MATHS
Evaluate: lim(x to 0^+)((e^(xln(2^(x-1))...

Evaluate: `lim_(x to 0^+)((e^(xln(2^(x-1)))-(2^x-1)^xsinx)/(e^(x lnx)))^(1/x)`

Promotional Banner

Topper's Solved these Questions

  • BOARD PAPER SOLUTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|65 Videos
  • DETERMINANTS

    RESONANCE DPP ENGLISH|Exercise All Questions|4 Videos

Similar Questions

Explore conceptually related problems

Evaluate : lim_(x to 0) (e^(x)-1)/x

Evaluate : lim_(x to 0) (e^(x) -e^(x))/x

Evaluate : lim_(xto0) (e^(x) -e^(-x))/x

Evaluate lim_(xto0) (e^(x)+e^(-x)-2)/(x^(2))

Evaluate : lim_(x to 0) (e^(cos x)-1)/(cos x)

lim_(xto0)((e^(x)-1)/x)^(1//x)

Evaluate: lim_(xto0)(log(e^(x)-x))/(1-cosx)

Evaluate lim_(xto0) (e^(x^(2))-cosx)/(x^(2))

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

Evaluate lim_(xto2) sin(e^(x-2)-1)/(log(x-1))

RESONANCE DPP ENGLISH-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^...

    Text Solution

    |

  2. Evaluate : ("lim")(xvec2a^+)(sqrt(x-2a)+sqrt(x)-sqrt(2a))/sqrt(x^2-4a^...

    Text Solution

    |

  3. Evaluate: lim(x to 0^+)((e^(xln(2^(x-1)))-(2^x-1)^xsinx)/(e^(x lnx)))...

    Text Solution

    |

  4. Let f(x)=[(sinx)/x]+[(2sin2x)/x]++[(10sin10 x)/x] (where [.] is the gr...

    Text Solution

    |

  5. The sum of the series x/(1!)+(2x^2)/(2!)+(3x^3)/(3!)+ is x e^x b. -x e...

    Text Solution

    |

  6. If a x^2+2h x y+b y^2=0, then (dy)/(dx) is equal to y/x (b) x/y (c) ...

    Text Solution

    |

  7. If f(x)=(log)x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e ...

    Text Solution

    |

  8. Let y=x^(3)-8x+7 and x=f(t)." If "(dy)/(dt)=2 and x=3 at t = 0," then ...

    Text Solution

    |

  9. If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) satisfy f(x)((dy)/(dx))^(3)=...

    Text Solution

    |

  10. Let f(x) ={{:((x-4)/(|x-4|)+a,xlt4),(a+b,x=4),( (x-4)/(|x-4|)+b, x gt4...

    Text Solution

    |

  11. The point(s) of minimum of function, f(x)=4x^3-x|x-2|,x in [0,3] is x=...

    Text Solution

    |

  12. Let g(x)=log(e)f(x) where f(x) is twice differentiable positive functi...

    Text Solution

    |

  13. Let f:""(1,""1)vecR be a differentiable function with f(0)""=""-1""a...

    Text Solution

    |

  14. If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...

    Text Solution

    |

  15. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

    Text Solution

    |

  16. If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove t...

    Text Solution

    |

  17. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) i...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...

    Text Solution

    |

  20. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)}...

    Text Solution

    |