Home
Class 11
MATHS
For x in R, lim(xrarroo)((x-3)/(x+2))^x...

For `x in R`, `lim_(xrarroo)((x-3)/(x+2))^x` is equal to (a) `e` (b) `e^(-1)` (c) `e^(-5)` (d) `e^5`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

lim_(xrarr0) (a^x-b^x)/(e^x-1) is equal to

lim_(x->0) ((1+x)^(1/x)-e)/x is equal to

lim_(x->0)(x(e^x-1))/(1-cosx) is equal to

("lim")_(xrarroo)(1/e-x/(1+x))^x is equal to (a) e/(1-e) (b) 0 (c) e/(e^(1-e)) (d) does not exist

lim_(x->oo)(1/e-x/(1+x))^x is equal to (a) e/(1-e) (b) 0 (c) e/(e^(1-e)) (d) does not exist

If lim_(xrarroo) ((x+c)/(x-c))^(x)=4 then the value of e^(c) is

int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C (d) x e^(-x)+C

lim_(x->0)(e^(5x) - 1)/(3x)

The value of lim_(xrarroo)[(e)/((1+(1)/(x))^(x))]^(x) is equal to

lim_(x->e) (lnx-1)/(x-e)

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. (lim)(xrarr0)(sin(picos^2x)/(x^2)) is equal to (a) -pi (b) pi (c) ...

    Text Solution

    |

  2. Evaluate lim(x->0^-) (x^2-3x+2)/(x^3-2x^2)

    Text Solution

    |

  3. For x in R, lim(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) ...

    Text Solution

    |

  4. Evaluate lim(n->oo) [sum(r=1)^n1/2^r] , where [.] denotes the gre...

    Text Solution

    |

  5. ("lim")(xvecoo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)}i se q u a lto 0 ...

    Text Solution

    |

  6. Evaluate ("lim")(x->(5pi)/4) [sinx+cosx], where [.] denotes the greate...

    Text Solution

    |

  7. If G(x)=-sqrt(25-x^2),t h e n lim(x->1)(G(x)-G(1))/(x-1)i s (a)1/(2...

    Text Solution

    |

  8. Evaluate the left-and right-hand limits of the function defined by f(...

    Text Solution

    |

  9. If f(x)=sqrt((x-sinx)/(x+cos^2x)), then lim (x->oo)f(x) is

    Text Solution

    |

  10. Evaluate the left-and right-hand limits of the function f(x)={(|x-4|)/...

    Text Solution

    |

  11. If ("lim")(x->a)[f(x)g(x)] exists, then both ("lim")(x->a)f(x)a n d("l...

    Text Solution

    |

  12. If alpha1, ,alpha2, ,alphan are the roots of equation x^n+n a x-b=0, ...

    Text Solution

    |

  13. lim(x->0)((xtan2x-2xtanx)/(1-cos2x)^2) is equal to

    Text Solution

    |

  14. Evaluate: ("lim")(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)

    Text Solution

    |

  15. lim(x->1)sqrt(1-cos2(x-1))/(x-1) a. exists and its equals sqrt(2) b....

    Text Solution

    |

  16. lim(x->0)sin^2(pi/(2-p x))^(sec^2((pi/(2-p x)))

    Text Solution

    |

  17. The value of lim(x->0)(sqrt(1/2(1-cos2x)))/x i s (a)1 (b) -1 (c...

    Text Solution

    |

  18. Evaluate: ("lim")(x->7/2)(2x^2-9x+8)^(cot(2x-7))

    Text Solution

    |

  19. If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):...

    Text Solution

    |

  20. Let f(a)=g(a)=k and their n t h derivatives exist and are not equal fo...

    Text Solution

    |