Question

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

Answer 1

The distance between `f(0)` and `f(1)` is `0.866`.

Explanation:

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

and for `f(1)` we have `(1/(1-3),1/sqrt(1^2+1))` or `(-1/2,1/sqrt2)`

The distance between the two points is

`sqrt((0-(-1/2))^2+(0-1/sqrt2)^2)=sqrt(1/4+1/2)=sqrt(3/4)=sqrt3/2=1.732/2=0.866`