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 This topic has been viewed 2242 times and has 4 replies
mikef3

Joined: Mar 14, 2012
Posts: 1
Status: Offline

I'm currently working on a calculus assignment and struggling with a few questions. I am asked to find the oblique asymptote of the function y= x-2Arctanx and can't seem to find it. Could anyone help me out?

Thanks,

Michael
 [Mar 14, 2012 2:16:58 PM] [Link]
pskinner

Joined: Apr 2, 2005
Posts: 797
Status: Offline

 I'm currently working on a calculus assignment and struggling with a few questions. I am asked to find the oblique asymptote of the function y= x-2Arctanx and can't seem to find it. Could anyone help me out? Thanks,Michael

For large x, -2arctanx approaches + or - 2*(pi/2)=+ or - pi. That is, it approaches a constant value on each side. On the other hand, for large x, x approaches infinity, and if you add + or - pi, it still approaches infinity...at the rate of x. So, the function is asymptotic to the line y=x. That is, y=x is the oblique asymptote. [Another way to look at it is that if you divide x-2arctanx by x and ask what happens at for large |x|, the expression approaches 1 so for large |x| they [the functions x-2arctanx and x] act similarly.
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Principal Skinner
 [Mar 17, 2012 8:19:44 AM] [Link]
williepitt

United States
Joined: Mar 26, 2012
Posts: 1
Status: Offline

I understood your solution a bit but can we plot a graph based on it?
 [Mar 27, 2012 12:17:18 AM] [Link]
pskinner

Joined: Apr 2, 2005
Posts: 797
Status: Offline

 I understood your solution a bit but can we plot a graph based on it?

Sure, plot both y=x,y=x-2*arctan(x) in the equation plotting calculator and you will "see" how the curve approaches the line:

http://webgraphing.com/plotting_basic.jsp
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Principal Skinner
 [Mar 31, 2012 10:37:48 AM] [Link]
RobertHarris

United States
Joined: Apr 6, 2012
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