Home
Class 11
MATHS
Use formula lim(x->0)(a^x-1)/x=log(a) to...

Use formula `lim_(x->0)(a^x-1)/x=log(a)` to find `lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)`

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

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

Evaluate: lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)

lim_(x->0)log(1+2x)/x

Evaluate lim_(x to 0) (2^(x)-1)/((1+x)^(1//2)-1)

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

Evaluate: lim_(x to 0)(3^(x)-1)/((4+x)^(1/2)-2)

lim_(x to 0) tan^-1x/x

If lim_(x to 0)x^((1)/(1-x))=e^(-1)

Evaluate: lim_(x->0)(x2^x-x)/(1-cosx)

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

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Given lim(x to 0)(f(x))/(x^(2))=2, where [.] denotes the greatest inte...

    Text Solution

    |

  2. Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not gr...

    Text Solution

    |

  3. Use formula lim(x->0)(a^x-1)/x=log(a) to find lim(x->0)(2^x-1)/((1+x)^...

    Text Solution

    |

  4. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

    Text Solution

    |

  5. f(x) is the integral of (2sinx-sin2x)/(x^3),x!=0. Find lim(x->0)f^...

    Text Solution

    |

  6. Evaluate underset (h to 0) lim ((a+h)^(2) sin (a+h) -a^(2) sin a)/h .

    Text Solution

    |

  7. underset(xtooo)lim(x(logx)^(3))/(1+x+x^(2)) equals

    Text Solution

    |

  8. underset(xto0)lim((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

    Text Solution

    |

  9. lim(x to 1) (1-x)tan((pix)/2)

    Text Solution

    |

  10. If f(x)={sinx ,x!=npi,n in I2,ot h e r w i s e g(x)={x^2+1,x!=0,4,x=...

    Text Solution

    |

  11. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

    Text Solution

    |

  12. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

    Text Solution

    |

  13. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a)...

    Text Solution

    |

  14. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

    Text Solution

    |

  15. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

    Text Solution

    |

  16. The value of lim(x->0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] repre...

    Text Solution

    |

  17. The value of lim(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-...

    Text Solution

    |

  18. The value of underset(xtooo)lim((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((...

    Text Solution

    |

  19. Let lim(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer....

    Text Solution

    |

  20. underset(xto1)lim(xsin(x-[x]))/(x-1), where [.] denotes the greatest i...

    Text Solution

    |