Home
Class 11
MATHS
Evaluate lim(xto(pi/3)) sqrt(1-cos6x)/(s...

Evaluate `lim_(xto(pi/3)) sqrt(1-cos6x)/(sqrt(2)(pi/3-x)`

Text Solution

Verified by Experts

Given, `underset(xto(pi/3))"lim"sqrt(1-cos6x)/(sqrt(2)(pi/3-x)) = underset(xto3)"lim"sqrt(1-1+2sin^(2)+3x)/(sqrt(2)(pi/3-x))` `[therefore cos2x=1-2sin^(2)x]`
`=underset(xto(pi)//3)"lim"(sqrt(2)sin3x)/(sqrt(2)(pi/3-x)=underset(xto(pi)/3)"lim"(sin3x)/(pi/3-x)` `[therefore cos2x=1-2sin^(2)x]`
`=underset(xto(pi)//3)"lim"(sqrt(2)sin3x)/(sqrt(2)(pi/3)-x) = underset(xto(pi)/3)"lim"(sin3x)/(pi/3-x)`
`=underset(xto(pi//3))"lim" (sin(pi-3x))/(pi-3x)=3 xx 1` `[therefore underset(xto0)"lim"(sinx)/(x) =1]`
=3 `[therefore xto(pi/3) rArr (x-pi/3)to 0]`
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|11 Videos

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise OBJECTIVE TYPE QUESTIONS|23 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|16 Videos

  • LINEAR INEQUALITIES

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|14 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(x->pi)(sqrt(1-cos6x))/(sqrt2(pi/3-x))

Evaluate, lim_(xto(pi//6)) (sqrt(3)sinx-cosx)/(x-pi/6)

Evaluate lim_(xto(pi)/(2)) (1+cos2x)/((pi-2x)^(2)).

Evaluate lim_(xto(pi)/(6)) (2-sqrt(3)cosx-sinx)/((6x-pi)^(2)).

Evaluate lim_(xto(pi)/(4)) (1-sin2x)/(1+cos4x).

Evaluate, lim_(xto(pi//4)) (sinx-cosx)/(x-pi/4)

Evaluate lim_(xto1) ("cos"(pi)/(2)x)/(1-sqrt(x))

Evaluate lim_(xto1) (x^(4)-sqrt(x))/(sqrt(x)-1) .

Evaluate lim_(xto oo)sqrt((x-sinx)/(x+cos^(2)x))

Evaluate lim_(xto oo)sqrt((x-sinx)/(x+cos^(2)x))