Question

Calculus. {arctan 2n}

Answer 1

Determine whether the sequence converges or diverges. If it converges, find the limit.

Answer 2

I know that arctan is bounded into (-pi/2 , pi/2). Does this mean that the answer is one of these?

Answer 3

That means your graph will lie in 1st and 4th quadrant only

Answer 4

\[f(n)=\tan^-1(2n)\]

Answer 5

so as n approached infinity, what does arctan do?

Answer 6

if n approaches infinity, so does 2n but we all know \[\tan(\frac{\pi}{2})=\]

Answer 7

i know that as n approaches zero, arctan approaches pi/2

Answer 8

\[\tan(\frac{\pi}{2})=infinity\]

Answer 9

thus as 2n approaches infinity, arctan approaches pi/2

Answer 10

as n approaches 0, arctan approaches 0 and not pi/2

Answer 11

ok i was thinking this:

Answer 12

but that is an angle i guess

Answer 13

So your question asks if \(a_n = \tan^{-1}(2n)\) converges or diverges?

Answer 14

yes and if it converges, what is the limit

Answer 15

nishant told me it is pi/2 and he i correct, cuz i checked... i was just hoping to get a visual of how that works is all

Answer 16

So doesnt the graph of inverse tangent just look like