(1 point) For each of the sequences below, enter either diverges if the sequence diverges, or the limit of the sequence if the sequence converges as n→[infinity]. (Note that to avoid this becoming a "multiple guess" problem you will not see partial correct answers.) A. sinn3n :

limit n→[infinity], sin(3n) neither converges nor diverges.

Detailed explanation below

Step-by-step explanation:

The trigonometric function/sequence sin(3n) continues to assume a periodic values as the values of n continue to increase. That is, n→[infinity]. sin(3n) neither diverges nor converges to a limit, uniformly. Rather, the sequence continue to diverge and converge repeatedly as n→[infinity].

This is because sin(3n) will form a periodic and oscillatory sequence as n tends to infinity.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)