Ap Calculus BC 2002 Form B Question 1?
a) Although it hasn't happened in recent years, it's always possible that the AP exam will ask you to graph something, perhaps a curve, a set of parametric equations, or even polar curves, so it's good to be ready!
What you have to do here is make a table of values. For instance, when
Thus you would plot the point
Don't forget the direction! Note that the particle is moving up because the y-coordinates are constantly increasing (since
b) The domain will be the domain of the x function, which will be
c) We only consider the x equation in this one. The first derivative is given by
Recall that speed is different than velocity; speed is given by
#s = sqrt((3cos(3t))^2 + 2^2) dt#
This is at
#s = sqrt(4) = 2#
d) Recall that distance travelled is given by
#d = int_(-pi)^pi sqrt((3cos(3t))^2 +4) dt#
Use a calculator to see that
#d ~~ 17.973#
And we can also verify that
Therefore, the distance travelled is indeed greater than
Hopefully this helps!