Question

For `f(t)= (lnt-e^t, t^2/e^t)` what is the distance between `f(2)` and `f(4)`?

Answer 1

with `f(t)=(ln(t)-e^t,t^2/e^t)` we get
`f(2)=(ln(2)-e^2,4/e^2)`
`f(4)=(ln(4)-e^4,16/e^4)`
so the distance is given by `sqrt((e^4-e^2-ln(2))^2+(4/e^2-16/e^4)^2)`

Explanation:

The distance between two points `P1(x1,y1)` and `P2(x2,y2)`
is given as `sqrt((x1-x2)^2+(y1-y2)^2)`