Undergraduate

Then we have r ( t ) = x ( t ) , y ( t ) = t , t 3 , 0 t

Then we have
r(t)=
x(t), y(t)
=
t, t3
,0 t 2.
Now we use
F(x, y)=xi 4yj =
x,4y
to find
F(r(t))= F(x(t), y(t)).
F(r(t))=
x(t),4y(t)
=
We also calculate
r'(t).
r(t)=
t, t3
r'(t)=
t,3t2

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