Question #d83b9

1 Answer
Dec 25, 2017

Lim_(xrarr0)(1-cosx)/(xsinx)=1/2

Explanation:

Lim_(xrarr0)(1-cosx)/(xsinx)*(1+cosx)/(1+cosx)

Lim_(xrarr0)(1^2-cos^2x)/(xsinx(1+cosx))

Lim_(xrarr0)(sin^2x)/(xsinx(1+cosx))

Lim_(xrarr0)(sinx)/(x(1+cosx))

Lim_(xrarr0)(sinx)/(x)=1

Lim_(xrarr0)(1)/(1+cosx)=1/(1+1)=1/2