Question

For `f(t)= (sqrt(t+2)/(t+1),t^2+3t)` what is the distance between `f(0)` and `f(2)`?

Answer 1

The distance between `f(0)` and `f(2)` is `10.028`.

Explanation:

The coordinates of point for `f(0)` is `(sqrt(0+2)/(0+1),0^2+3xx0)` or `(sqrt2,0)`

and for `f(2)` we have `(sqrt(2+2)/(2+1),2^2+3xx2)` or `(2/3,10)`

The distance between the two points is

`sqrt((sqrt2-2/3)^2+(0-10)^2)=sqrt(0.74755^2+100)=10.028`