An object moving along a curve in the xy-plane has position (x(t), y(t)) at time t with dx/dt = cos(t^3) and dy/dt 3sin(t^2) for 0<= t<= 3. At time t=2, the object is at position (4,5).(adsbygoogle = window.adsbygoogle || []).push({});

a. Write an equation for the line tangent to the curve at (4,5).

b. Find the speed of the object at time t=2.

c. Find the total distance traveled by the object over the time interval 0<=t<=1.

d. Find the position of the object at time t=3.

a. I found the slope by 3sin(t^2)/cos(t^3) (t->2)

I get 15.6

so y-5=15.6(x-4)?

b. Sqrt[(x'(t))^2 + (y'(t)^2)]

so I just squared the givens (with t=2)

= 2.3166 ?

c. Integral (0 to 1) Sqrt[(cos(t^3))^2 + (3sin(t^2))^2]

= 1.458

d. Not sure what to do about this part...

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# Find the total distance traveled by the object

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