Home
Class 11
MATHS
Evaluate lim(xto0) (1-cos2x)/x^(2)...

Evaluate `lim_(xto0) (1-cos2x)/x^(2)`

A

2

B

1

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `underset(xto0)"lim"(1-cos2x)/x^(2) = underset(xto0)"lim"(1-1+2sin^(2)x)/(x^(2))` `[therefore cos2x=1-2sin^(2)x]`
`=underset(xto0)"lim"(2sin^(2)x)/(x^(2))=2 underset(xto0)"lim"(sin^(2)x)/(x^(2))`
`=2underset(xto0)"lim"((sinx)/x)^(2)` `[therefore underset(xto0)"lim"(sinx)/x=1]`
`=2 xx 1=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) (logcosx)/(x)

Evaluate lim_(xto0)(1-cos2x)/(1-cos4x)

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

Evaluate lim_(xto0) (1-cos(1-cosx))/(x^(4)).

Evaluate lim_(xto0)(cosecx)^(x) .

Evaluate lim_(xto0) (cos^(-1)((1-x^(2))/(1+x^(2))))/(sin^(-1)x).

Evaluate lim_(xto0) sin(picos^(2)x)/(x^(2)).

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

Evaluate lim_(xto0) (2sinx-sin2x)/(x^(3))