F'(t) 4 6 2 1
t 0 1 2 3

Find f(1)-f(0)

W

s

=6

W

t

=−36

Step-by-step explanation:

u v

u(1, -9) = 3v(1, -9) = 0u(1,−9)=3v(1,−9)=0

us(1, -9) = 9vs(1, -9) = -6us(1,−9)=9vs(1,−9)=−6

ut(1, -9) = 4vt(1, -9) = 7ut(1,−9)=4vt(1,−9)=7

Fu(3, 0) = -2Fv(3, 0) = -4Fu(3,0)=−2Fv(3,0)=−4

To find W_{s}W

s

Now we can apply the above expression

W(s, t) = F(u(s, t), v(s, t))

(1,-9)=((u(1, -9), v(1, -9)), (u(1, -9), v(1, -9))) · ((1, -9), (1, -9))

=(F_{u}F

u

(3, 0), F_{v}F

v

(3, 0)) · (9, -6)

\begin{gathered}=(-2,-4).(9,-6)\\=(-18)+(24)\\=6\end{gathered}

=(−2,−4).(9,−6)

=(−18)+(24)

=6

To find W_{t}W

t

:

(1,-9)=((u(1, -9), v(1, -9)), (u(1, -9), v(1, -9))) · ((1, -9), (1, -9))

= (F_{u}F

u

(3, 0), F_{v}F

v

(3, 0)) · (4, 7)

\begin{gathered}=(-2,-4).(4,7)\\=(-8)+(-28)\\=-36\end{gathered}

=(−2,−4).(4,7)

=(−8)+(−28)

=−36

the circumference is c≈245.04