Home
Class 11
MATHS
Evaluate lim(xto0) ((x+2)^(1//3)-2^(1//3...

Evaluate `lim_(xto0) ((x+2)^(1//3)-2^(1//3))/(x)`

A

`1/(3)(2)^(2//3)`

B

`1/(3.(2)^(2//3))`

C

`1/(3)`

D

none of the above

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `underset(xto0)"lim"((x+2)^(1//3)-2^(1//3))/(x) = underset(xto0)"lim"((x+2)^(1//3)-2^(1//3))/((x+2)-2)`
`=1/3 xx 2^(1//3-1)`
`=1/3 xx (2)^(-2//3)` `[therefore underset(xtoa)"lim"(x^(n)-a^(n))/(x-a) = na^(n-1)]`
`=1/(3(2)^(2//3))` `[therefore x to 0 rArr x+2 to 2]`
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|11 Videos

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|23 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Fillers|16 Videos

  • LINEAR INEQUALITIES

    NCERT EXEMPLAR|Exercise Objective Type Questions|14 Videos

Similar Questions

Explore conceptually related problems

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

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

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

Evaluate lim_(xto0)(3^(2x)-2^(3x))/(x).

Evaluate lim_(xto0)(sqrt(1+x)-1)/(x)

Evalaute lim_(xto0) (x2^(x)-x)/(1-cosx)

Evaluate lim_(xto0)x^(3)"cos"2/x .

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

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

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