(i) At 1 Measureing Functions
At 1 - Sorry I did not post this at 1 the first time -
1) Study the two red points
2) Notice all the Tangent Lines as the slider moves from 1 to 8
3) At 8 the Green Circle is 4 Pi - At 1 ; Vector " v " fits in between the Ln x and the 2nd derivative of the 2^x.
4) This measures the Functions perfectly