Can anyone help me with this? Graph f(x)=1+2arctg(x−2); find the derivative of...

[mattes101]

Can anyone help me with this? Graph f(x)=1+2arctg(x−2); find the derivative of...

 

[ksdhart2]

1) Draw a graph, determine the domain and mark the intersections with the axes: \(\displaystyle f(x)=1+2arctg(x-2)\)

Okay, so this seems to be a fairly straightforward exercise of graphing a function. I'll assume you're not having any difficulties with this.

2) Write the derivative of the following function: \(\displaystyle f(x)=ln \left(\dfrac{x+1}{x-1} \right)\)

For this one, I think a good first step would be to use a formula you [should have] learned way back in algebra: \(\displaystyle ln \left( \dfrac{a}{b} \right)=ln(a)-ln(b)\). Where does that lead? What do you think a good next step would be?

3) Sketch [the] graph of the following function: \(\displaystyle f(x)=\dfrac{2x}{x^2+1}\)

This is another straightforward graphing problem.

4) Determine the following integral: \(\displaystyle \int \dfrac{8x-31}{x^2-9x+14} \: dx\)

A good first step here would be to factor the denominator. Does that perhaps suggest a good value to use for u-substitution? Maybe one of those factors?

For all of these problems, please include any and all work you've done on them, even if you know it's wrong. The more specific you can be about exactly what you've already tried and exactly where you're getting stuck, the better help we can provide. Thank you.

 

[HallsofIvy]

A good first step here would be to factor the denominator. Does that perhaps suggest a good value to use for u-substitution? Maybe one of those factors?

"Partial fractions" first!