Consider g(ξ) = [(2H)/π] arctan(ξ).
Plot a graph of the function g(ξ).
Imagine a line that passes through the point on the curve at ξ0 = 1.30, and which is tangent to the curve at that point. Where does the tangent line intersect the vertical axis?
[DATA: H = 2.00 ; ξ0 = 1.30 .]
The Attempt at a Solution
Firstly I know that H=2 so I can easily simplify the question to (4/π)*arctan(ξ).
I then want to find the slope so I take the derivative of that function and get 4/(πξ^2+π) then plug in ξ=1.3 to find the slope at that point. The result is: 0.473323
I can also plug ξ=1.3 into the original equation to find the y value at that point. The result is: 1.16514
Plugging in those values to y=mx+b I get 1.16514=(.473323)(1.3)+b. The resulting y-intercept (b) is 1.89.
Unfortunately, this is not correct! I am obviously making a silly mistake somewhere. Is anyone able to point out what I did wrong?