Home
Class 12
MATHS
Evaluate lim(x to 0) ((sinx)/(x))^(((sin...

Evaluate `lim_(x to 0) ((sinx)/(x))^(((sinx)/(x-sinx))).`

Text Solution

Verified by Experts

Since, `underset(xto0)lim(sinx)/(x)=1`
and `" "underset(xto0)lim(sinx)/(x-sinx)=underset(xto0)lim(1)/(((x)/(sinx)-1))=(1)/(1-1)=oo`
we have `underset(xto0)lim((sinx)/(x))^(((sinx)/(x-sinx)))=e^(underset(xto0)lim((sinx)/(x)-1)((sinx)/((x-sinx))`
`=e^(underset(xto0)lim-(sinx)/(x))=e^(-1)=(1)/(e)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate ("lim")_(xvec0)((sinx)/x)^(((sinx)/(x-sinx)))

Evaluate lim_(xtooo) (sinx)/(x).

Evaluate lim_(xto0) (sinx-x)/(x^(3)).

Evaluate lim_(xto0)|x|^(sinx)

Evaluate lim_(x to oo) (sinx^(0))/(x).

Evaluate lim_(xto0^(+))(sinx)^(x)

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

Evaluate lim_(x to 0) (sinx-2)/(cosx-1).

The value of lim_(xrarr0) ((sinx)/(x))^((sinx)/(x-sinx)) , is

Evaluate lim_(xto0)(tanx-sinx)/(x^(3)).