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

1 Answer
Mar 8, 2018

Answer:

# 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#.