Home
Class 12
MATHS
lim ( x to 0) (e ^(sin (x ))-1)/(x ) eq...

`lim _( x to 0) (e ^(sin (x ))-1)/(x )` equals to :

A

1

B

2

C

e

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|16 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|14 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|5 Videos

Similar Questions

Explore conceptually related problems

lim_(x to 0) (2 sin x - sin 2x)/(x^(3)) ie equal to

lim_(x to 0) (sin x^(@))/( x) is equal to

Evaluate lim_(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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

lim_(x to 0) (sin^(2) x//4)/(x) is equal to

lim_(x to 0) (sin 3x)/(x) is equal to

lim_(xto0) (sin(picos^(2)x))/(x^(2)) is equal to

lim_(xrarr0)((1-e^x)sin x )/(x^2+x^3) is equal to

lim_(xto0)(|sin x|)/x is equal to :

If lim_(xto0)(f(x))/(sin^(2)x)=8,lim_(xto0)(g(x))/(2cosx-xe^(x)+x^(3)+x-2)=lamda" and " lim_(x to 0)(1+2f(x))^((1)/(g(x)))=(1)/(e)," then" lim_(x to 0)(1+f(x))^((1)/(2g(x))) is equal to

VIKAS GUPTA (BLACK BOOK) ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. lim ( x to 0) (e ^(sin (x ))-1)/(x ) equals to :

    Text Solution

    |

  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

    Text Solution

    |

  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

    Text Solution

    |

  4. Let f (x) = x cos x, x in [(3pi)/(2), 2pi] and g (x) be its inverse. ...

    Text Solution

    |

  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

    Text Solution

    |

  6. If the value of the definite integral int ^(-1) ^(1) cos ^(-1) ((1)/(s...

    Text Solution

    |

  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

    Text Solution

    |

  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

    Text Solution

    |

  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2)+1))")")dx...

    Text Solution

    |

  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

    Text Solution

    |

  11. Find the value of |a| for which the area of triangle included between ...

    Text Solution

    |

  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

    Text Solution

    |

  13. If I = int (0) ^(100) (sqrtx)dx, then the value of (9I)/(155) is:

    Text Solution

    |

  14. Let I(n) = int (0)^(pi) (sin (n + (1)/(2))x )/(sin ((x)/(2)))dx where ...

    Text Solution

    |

  15. If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

    Text Solution

    |

  16. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

    Text Solution

    |

  17. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

    Text Solution

    |

  18. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

    Text Solution

    |

  19. Given a function g, continous everywhere such that g (1)=5 and int (0)...

    Text Solution

    |

  20. If f (n)= 1/pi int (0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2)...

    Text Solution

    |

  21. Let f (2-x) =f (2+xand f (4-x )= f (4+x). Function f (x) satisfies int...

    Text Solution

    |