- #1

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this is not homework. i'm trying to learn how to do it.

EDIT:

and is there anything like

__3 sequence theorems__?

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- Thread starter lalapnt
- Start date

- #1

- 12

- 0

this is not homework. i'm trying to learn how to do it.

EDIT:

and is there anything like

- #2

tiny-tim

Science Advisor

Homework Helper

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hi lalapnt! welcome to pf!

how do you find the limit of this:

[PLAIN]http://www.matematyka.pl/latexrender/pictures/f/2/f2f7060d34f6c6a8b77a07d90e8c9b8f.png[/QUOTE] [Broken]

just draw the graph of tanx

then mark the positions of arctan100, arctan1000, etc …

where are they heading to? EDIT:

and is there anything like3 sequence theorems?

sorry, not folloowing you

Last edited by a moderator:

- #3

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- #4

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i want to know how to prove it. @haruspex

@tiny-tim do you have an idea what this is:

- #5

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Firstly, you have to know how to draw the graph of such funtions as (log, tang, cot, sin, cos...) then try to draw the inverse graph of these functions. You should also know about limit and its theorems. That's how I try to find a way to solve that kind of problems.

Now your question's solution:

[itex]\lim_{x\rightarrow+∞}arctgx =?[/itex]

When you draw the graph of arctgx and take the limit x goes to positive infinity, the function converges [itex]\frac{\pi}{2}[/itex]. Eventually, we conclude the answer is

[itex]\lim_{x\rightarrow+∞}arctgx = \frac{\pi}{2}[/itex]

Now your question's solution:

[itex]\lim_{x\rightarrow+∞}arctgx =?[/itex]

When you draw the graph of arctgx and take the limit x goes to positive infinity, the function converges [itex]\frac{\pi}{2}[/itex]. Eventually, we conclude the answer is

[itex]\lim_{x\rightarrow+∞}arctgx = \frac{\pi}{2}[/itex]

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- #6

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For a formal proof, a starting point has to be a definition of the atan function. Having chosen one, can you prove tan(y) >= y for 0 < y < pi/2? From there it's not hard.i want to know how to prove it.

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