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sketching a graph watch

1. hey

so the question asks to sketch a graph of f, a function defined by f(x) = x - arctanx, showing cleary all the asymptotes.

By finding the second derivative of f, it shows that it has a point of inflexion at (0,0), concave down when x<1, and concave up when x>1. For the asymptotes i know that when arctanx = pi/2, then x is infinite, but how can i draw this exactly?

*this question is non- calculator btw.

thanks
2. When x is large and positive, arctan x tends to pi/2, so f(x) is approximately x - pi/2. So you could include y=x-pi/2 as an asymptote. Do a similar thing for when x gets very negative.
3. (Original post by ttoby)
When x is large and positive, arctan x tends to pi/2, so f(x) is approximately x - pi/2. So you could include y=x-pi/2 as an asymptote. Do a similar thing for when x gets very negative.
thank you

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Updated: April 11, 2011
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