(b)
(c)
(d)
(a)
(b)
(b)
(c)
(a)
(b)
What is the radius of convergence of the series in (a)?
Use the first five terms in (a) to approximate ln(1.2).
Estimate the error in (c), justifying your answer.
A cycloid is given parametrically by x = θ − sin θ, y = 1 − cos θ.
Find the slope of the curve at the point where .
Find the equation of the tangent to the cycloid at the point where
.
Find the area of the region enclosed by both the polar curves r = 4 sin θ
and r = 4 cos θ.
(a) Find the 4th degree Taylor polynomial about 0 for cos x.
Use part (a) to evaluate cos x dx.
Estimate the error in (b), justifying your answer.
A particle moves on the curve of y^3 = 2x + 1 so that its distance from the
x-axis is increasing at the constant rate of 2 units/sec. When t = 0, the
particle is at (0,1).
Find a pair of parametric equations x = x(t) and y = y(t) that describe
the motion of the particle for nonnegative t.
Find |a|, the magnitude of the particle’s acceleration, when t = 1.
Find the area of the region that the polar curves r = 2 − cos θ and r = 3
cos θ enclose in common.
