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WebGraphing.com Forum » List all forums » Forum: Calculus Homework Help » Thread: Inverse Trig |
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Total posts in this thread: 5 |
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mikef3
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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 |
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pskinner
Joined: Apr 2, 2005 Posts: 797 Status: Offline |
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. ---------------------------------------- Principal Skinner |
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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? |
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pskinner
Joined: Apr 2, 2005 Posts: 797 Status: Offline |
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 ---------------------------------------- Principal Skinner |
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RobertHarris
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Thanks for explaining a graph in details Mr. Skinner. The coordinates are helpful to build a graph. ---------------------------------------- Buy kitchen cabinets |
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Re: Inverse Trig