Home
Class 11
MATHS
The value of a, b and c such that lim(...

The value of a, b and c such that
`lim_(x rarr 0) (ae^x -b cosx + ce^(-x))/(x sinx) = 2` are

A

a=1,b=-2, c=1

B

a=1,b=2, c=-1

C

a=1,b=2, c=1

D

a=-1,b=2, c=1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Evaluate lim_(x rarr 0) [e^(px) - e^(-qx])/x

lim_(x rarr 0)(x^(n) ln x), n gt 0

Evaluate: lim_(x rarr 0) ((e^(x)-1)log(1+x))/(sin^(2)x)

Evaluate: lim_(x rarr 0)(e^(13x)-e^(7x))/(x)

Evaluate: lim_(x rarr 0) ((e^(2)-1)log(1+x))/(sinx)

Show that , lim_(x rarr 0)(3^(x)+3^(-x)-2)/(x^(2)

Evaluate: lim_(x rarr 0)(a^(alphax)-b^(betax))/(x)

The value of lim_(x rarr 0) (1-cos2x)/(e^(x^(2))-e^(x)+x) is

lim_(x rarr 0) ((1+tan x)/(1-tan x))^(1/x) is

lim_(x to 0) (1-cosx)/x^2 = ?

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The value of lim(x rarr 0) |cosx + sinx|/x^2 is equal to

    Text Solution

    |

  2. lim(x rarr infty)(root(2)(x^2 + 1)-root(3)(x^2 + 1))/(root(4)(x^2 + 1)...

    Text Solution

    |

  3. The value of a, b and c such that lim(x rarr 0) (ae^x -b cosx + ce^(...

    Text Solution

    |

  4. Let f(x) = lim(n rarr infty)(sinx)^(2n), then f is

    Text Solution

    |

  5. The set of all points where the function f(x)= x/(1+|x|) is differenti...

    Text Solution

    |

  6. Let f(x) = (x(1+a cosx) - b sinx)/x^2, x ne 0 and f(0) = 1

    Text Solution

    |

  7. If x + |y| = 2y, then y as a function of x is :

    Text Solution

    |

  8. Let [x] denotes the greatest integer less than or equal to x, If (x) =...

    Text Solution

    |

  9. The function f(x) = {(|x-3|, x ge 1), (x^2/4-(3x)/2+13/4, x lt1):}

    Text Solution

    |

  10. Which of the following functions are continuous on (0, pi):

    Text Solution

    |

  11. If f(x) = "min"{1, x^2, x^3} then :

    Text Solution

    |

  12. Let f(x) be defined in [-2, 2] by f(x) = "maximum" (sqrt(4-x^2), sqr...

    Text Solution

    |

  13. If lim(x rarr 0)((a^x+b^x+c^x)/3)^(lambda/x), (a, b, c, lambda gt o) i...

    Text Solution

    |

  14. If f(x)=(|x|/(2 + |x|))^(2x), then

    Text Solution

    |

  15. Let f(x) = {(1+(2x)/lambda, o le x le 1), (lambda x, 1 le x le 2):} ...

    Text Solution

    |

  16. If m, n in N, lim x tends to 0 '(sin(x^m)/sin(x^n))​' (m, n∈N)=0, lf

    Text Solution

    |

  17. Let f(x) = (1-cos4x)/x^2, g(x) sqrtx/(sqrt(16+sqrtx)-4) and phi(x) ...

    Text Solution

    |

  18. Let f(x) = (1-cos4x)/x^2, g(x) sqrtx/(sqrt(16+sqrtx)-4) and phi(x) ...

    Text Solution

    |

  19. Let f(X) = lfloorxrfloor - lceilingxrceiling for all x in R Answer t...

    Text Solution

    |

  20. Let f(X) = lfloorxrfloor - lceilingxrceiling for all x in R Answer t...

    Text Solution

    |