Home
Class 11
MATHS
Evaluate the following limit: lim(x->0)(...

Evaluate the following limit: `lim_(x->0)(e^(sinx)-1)/x`

Text Solution

Verified by Experts

`lim_(x->0)(e^(sinx)-1)/x`
`=lim_(x->0)((e^(sinx)-1)/sinx)/(x/(sin x))`

`=(lim_(x->0)((e^(sinx)-1)/sinx))/(lim_(x->0) (1/((sin x)/x))`

`=1/1`
`=1`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA|Exercise Solved Examples And Exercises|114 Videos
  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limits : lim_(x to 0)(e^(sinx)-1)/x

Evaluate the following limits : lim_(x to 0)(e^(sinx)-1)/sinx

Evaluate the following limit: (lim)_(x->0)(e^(sin2x)-e^(sin\ x))/x

Evaluate the following limits : lim_(x to 0)(e^(sin2x)-e^(sinx))/x

Evaluate of the following limit: (lim)_(x->0)(x-sinx)/(x^3)

Evaluate the following limits: lim_(xrarr0)((e^(tanx)-1))/(x)

Evaluate the following limits : lim_(x to 0)e^(x)

Evaluate the following limits: lim_(xrarr0)((e^(x)-x-1)/(x))

Evaluate the following limits: lim_(xrarr0)((e^(4x)-1)/(x))

Evaluate the following limits: lim_(xrarr0)((2^(x)-1)/(x))