Find the limit as x --> + infinity and – infinity for the following:?

[Bejsan]

Find the limit as x à + infinity and – infinity for the following:

y = ( x sin x + 2 sin x) / 6x^2

HELP PLEASE

 

[JessicaB]

lim(x->inf )( x sin x + 2 sin x) / 6x^2
= lim(x->inf)[sin(x)/6x].lim(x->inf)[sin(x)/3x^2)
= (1/6)*lim(x->inf)[sin(x)/x].(1/3)lim(x->inf)[sin(x)/x].lim(x->inf) (1/x)
= 0 {as lim(x->inf)[sin(x)/x]=0}

Also;
lim(x->-inf )( x sin x + 2 sin x) / 6x^2
= (1/6)*lim(x->-inf)[sin(x)/x].(1/3)lim(x->-inf)[sin(x)/x].lim(x->-inf)[1/x]
= 0 {since the lim(x->-inf)[1/x]=0}