Question

For `f(t)= (e^(t^3-t^2), te^t )` what is the distance between `f(0)` and `f(1)`?

Answer 1

`e`

Explanation:

Find each point:

`f(0)=(e^(0^3-0^2),0e^0)=(e^0,0)=(1,0)`

`f(1)=(e^(1^3-1^2),1e^1)=(e^0,e)=(1,e)`

Since these points lie on the same vertical axis, we can determine the distance without having to use the distance formula:

`e-0=e`