Question

For `f(t)= (lnt-e^t, t^2e^t)` what is the distance between `f(1)` and `f(2)`?

Answer 1

`sqrt((ln(2)-e^2+e)^2+(4e^2-e)^2)~~27.131`

Explanation:

`f(1) = (ln(1)-e^1, 1^2*e^1) = (-e,e)`

`f(2) = ln(2)-e^2, 2^2*e^2) = (ln(2)-e^2,4e^2)`

The distance between two points `(x_1, y_1)` and `(x_2, y_2)` is given by `sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

Thus, the distance between `f(1)` and `f(2)` is

`sqrt((ln(2)-e^2+e)^2+(4e^2-e)^2)~~27.131`