Home
Class 11
MATHS
lim(x->0) {(1+x)^(2/x)} (where {.} denot...

`lim_(x->0) {(1+x)^(2/x)}` (where {.} denotes the fractional part of x (a) `e^2−7` (b) `e^2−8` (c) `e^2−6` (d) none of these

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_(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part of x) is equal to

lim_(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional part of x is equal to

lim_(x->∞) (log_e[x])/x where [.] denotes the gif is

The period of function 2^({x})+sinpix+3^({x/2})+cos2pix (where {x} denotes the fractional part of (x) is 2 (b) 1 (c) 3 (d) none of these

lim_(xrarroo) {(e^(x)+pi^(x))^((1)/(x))} = (where {.} denotes the fractional part of x ) is equal to

The total number of solution of sin{x}=cos{x} (where {} denotes the fractional part) in [0,2pi] is equal to 5 (b) 6 (c) 8 (d) none of these

The total number of solution of sin{x}=cos{x} (where {} denotes the fractional part) in [0,2pi] is equal to 5 (b) 6 (c) 8 (d) none of these

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to (a) -2 (b) -1 (c) 0 (d) none of these

lim x→(2^+) { x } sin( x−2 ) /( x−2)^2 = (where [.] denotes the fractional part function) a. 0 b. 2 c. 1 d. does not exist

int_0^2 x^3[1+cos((pix)/2)]dx , where [x] denotes the integral part of x , is equal to (A) 1/2 (B) 1/4 (C) 0 (D) none of these

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Let f(x)=("lim")(nvecoo)1/((3/pitan^(-1)2x)^(2n)+5)dot Then the set of...

    Text Solution

    |

  2. Evaluate (lim(x->oo))(x(log)e{(sin(a+1/x))/(sina)}), 0 lt a lt pi/2

    Text Solution

    |

  3. lim(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x (a...

    Text Solution

    |

  4. Evaluate: ("lim")(xvec0)(2^x-1)/(sqrt(1+x)-1)

    Text Solution

    |

  5. If f(n+1)=1/2{f(n)+9/(f(n))},n in N , and f(n)>0 for all n in...

    Text Solution

    |

  6. Evaluate underset(xto1)lim(a^(x-1)-1)/(sinpix).

    Text Solution

    |

  7. Find ("lim")(xvecoo)(5x+2cosx)/(3x+14) using sandwitch theorem

    Text Solution

    |

  8. Evaluate: [("lim")(xto0)(tanx)/x] where [dot] represents the greatest...

    Text Solution

    |

  9. If lim(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the value of x.

    Text Solution

    |

  10. Evaluate: ("lim")(xvec0)(tanx)/x where [dot] represents the greatest ...

    Text Solution

    |

  11. Evaluate underset(xto0)lim(e^(x)-e^(xcosx))/(x+sinx).

    Text Solution

    |

  12. Evaluate: ("lim")(xvec2)(x-2)/((log)a(x-1))

    Text Solution

    |

  13. Evaluate: lim(n->0)(e^(sinx)-(1+sinx))/({tan^(-1)(sinx)}^2)

    Text Solution

    |

  14. Evaluate: ("lim")(x->a)(logx-loga)/(x-a)

    Text Solution

    |

  15. Evaluate: (lim)(x->(3pi)/4)(1+(tanx)^(1/3))/(1-2cos^2x)

    Text Solution

    |

  16. Evaluate: "lim"(x->0)(10^x-2^x-5^x+1)/(xtanx)

    Text Solution

    |

  17. ("lim")(xvec1)((x^4+x^2+x+1)/(x^2-x+1))^(1-"cos"(x+1))/((x+1)^(2))i se...

    Text Solution

    |

  18. Evaluate: "lim"(x->0)(3^(2x)-2^(3x))/x

    Text Solution

    |

  19. ("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(...

    Text Solution

    |

  20. Evaluate: ("lim")(xvec0)(log(5+x)-"log"(5-x))/x

    Text Solution

    |