Home
Class 12
MATHS
The value of Lim(xto0) ((e)/(4x)-(e)/(2x...

The value of `Lim_(xto0) ((e)/(4x)-(e)/(2x(e^(ex)+1)))` equals

A

`(e^(2))/(2)`

B

`(e^(2))/(4)`

C

`(e^(2))/(8)`

D

`(e)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xto0)Lim((e)/(4x)-(e)/(2x(e^(ex)+1)))=underset(xto0)Lim(e)/(4x)(1-(2)/(e^(ex)+1))=underset(xto0)Lim(e)/(4x)((e^(ex)+1-2)/((e^(ex)+1)))=(e^(2))/(8)underset(xto0)Lim((e^(ex)-1))/(ex)=(e^(2))/(8)`.
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    BANSAL|Exercise MATHS SECTION-3 PART-B [MULTIPLE CORRECT CHOICE TYPE]|5 Videos

  • TEST PAPERS

    BANSAL|Exercise MATHS SECTION-3 PART-C [INTEGER TYPE]|5 Videos

  • TEST PAPERS

    BANSAL|Exercise CHEMISTRY SECTION-2 PART-C [INTEGER TYPE]|5 Videos

  • PROBABILITY

    BANSAL|Exercise All Questions|1 Videos

  • THERMODYNAMICS

    BANSAL|Exercise Match the column|7 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(x to 0)(e^(4x)-1)/x is :

The value of lim_(x to 0)(e^(2x)-1)/(x) is :

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

The value of lim_(xto0)(e^(x)-e^(x cosx))/(x+sinx) is

The value of lim_(xto 0)(e-(1+x)^(1//x))/(tanx) is

lim_(xto0)((e^(x)-1)/x)^(1//x)

Evaluate lim_(xto0) (e^(x)+e^(-x)-2)/(x^(2))

The value of lim_(x rarr0)((e^(1/x^(2))-1)/(e^(1/x^(2)+1))) is :

Slove lim_(xto0)((1+x)^(1//x)-e)/x