Question

Find the limit of the sequence or state it does not exist.

Answer 1

\[\frac{ \tan ^{-1}n }{ n }\]

Answer 2

It does not exist.

Answer 3

why do you say that

Answer 4

\[\lim_{n\to \infty}\tan^{-1}(n)=\frac{\pi}{2}\] does that help?

Answer 5

Yes, that does but how did you it was pi/2?

Answer 6

think of what the graph looks like!

Answer 7

Oh right I got it thanks!

Answer 8

or think that \(\tan(x)\) has a vertical asymptote at \(\frac{\pi}{2}\)

Answer 9

the graph goes from -pi/2 to pi/2 and since we are taking the limit from positive infinite it will be pi/2

Answer 10

yes