Question

For `f(t)= (e^t/t,4t+1/t)` what is the distance between `f(2)` and `f(5)`?

Answer 1

The distance is `sqrt(4e^10-20e^7+25e^4+117)/10`

Explanation:

we will substitute first 2 and then 5:

`f(2)=(e^2/2,4*2+1/2)=(e^2/2,17/2)`

`f(5)=(e^5/5,4*5+1/5)=(e^5/5,101/5)`

Then we will apply the distance formula:

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

`d=sqrt((e^5/5-e^2/2)^2+(101/5-17/2)^2)`

`=sqrt(((2e^5-5e^2)/10)^2+((101*2-17*5)/10)^2)`

`=sqrt((4e^10-20e^7+25e^4)/100+(202-85)/100)`

`=sqrt(4e^10-20e^7+25e^4+117)/10`