Home
Class 12
MATHS
underset(x rarr 0)lim (sin alpha x)/(e^(...

`underset(x rarr 0)lim (sin alpha x)/(e^(beta x) - 1) (alpha, beta != 0)` equal to -

A

`(beta)/(alpha)`

B

0

C

`(alpha)/(beta)`

D

limit does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CALCULUS

    CHHAYA PUBLICATION|Exercise WBHS Archive (2016)|7 Videos
  • CALCULUS

    CHHAYA PUBLICATION|Exercise WBJEE Archive (2013)|2 Videos
  • CALCULUS

    CHHAYA PUBLICATION|Exercise WBHS Archive (2014)|6 Videos
  • BINOMIAL THEOREM

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion -Reason Type)|2 Videos
  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (E. Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

lim_(xrarr0)(sinalphax)/(e^(betax)-1)(alpha,beta!=0) equals to

Prove : underset(xrarr0)"lim"(sinalphax^(@))/(sinbetax^(@))=(alpha)/(beta)

Knowledge Check

  • The value of underset(x rarr 0)lim (sin 5x)/(tan 3x) is

    A
    2
    B
    5
    C
    `(5)/(3)`
    D
    `(3)/(5)`
  • underset(x rarr 0)lim (sin(pi cos^(2) x))/(x^(2)) is equal to -

    A
    `(pi)/(2)`
    B
    1
    C
    `-pi`
    D
    `pi`
  • If underset(x rarr 0)lim (2a sin x - sin 2x)/(tan^(3)x) exists and is equal to 1, then the value of a is -

    A
    2
    B
    1
    C
    0
    D
    `-1`
  • Similar Questions

    Explore conceptually related problems

    Evaluate: underset(x rarr 0)lim(log_e(1+alphax)/(e^(2x)-1))

    Prove that underset(x rarr 0)lim (log(1+x)+sinx)/(e^x-1) =2

    Evaluate : underset(x rarr 0)lim (sin(x^(2)-x))/x

    Let , alpha, beta in RR be such that underset(x rarr 0)lim (x^(2) sin (beta x))/(alpha x - sin x) = 1 . Then 6(alpha + beta) equals

    underset(x rarr 0)lim ((1-cos 2x) (3+cos x))/(x tan 4x) is equal to -