What is the value of lim_(x->0) (1-cos(mx))/(xsinx)?

1 Answer
Mar 8, 2018

m^2/2.

Explanation:

"The Reqd. Lim.="lim_(x to 0)(1-cosmx)/(xsinx),

=lim_(x to 0){2sin^2((mx)/2)}/(xsinx),

=lim2{sin((mx)/2)/((mx)/2)*((mx)/2)}^2-:{x((sinx)/x*x)},

=lim2{sin((mx)/2)/((mx)/2)}^2*(m^2x^2)/4-:{x^2(sinx/x)},

=(2*m^2/4)*lim_((mx)/2 to 0){sin((mx)/2)/((mx)/2)}^2-:lim_(x to 0){(sinx/x)},

=m^2/2*(1)^2-:1.

rArr "The Reqd. Lim.="m^2/2.