Question

1.
Find the arclength of r=cos^(3)(theta/3)

2. Find the area outside r=3 and inside
r^2=18cos(2•theta)

3. Find the slope of the tangent line to r=2sin(4•theta) at
theta=pi/4

Answer #1

Find the area inside of r=1+cos theta, but outside of r=1+sin
theta

Find the area of the region that is outside the cardioid r = 1
+cos (theta) and inside the circle r = 3 cos (theta), by
integration in polar coordinates.

1. Find the slope of the tangent line to
r=2+sin3Θ at the point where
Θ=pi/4 Θ=theta
2. Find the area of the region that lies inside the
curve r=4*sinΘ and outside the curve r=2

Find the area inside r=3 and outside r=3sin 3 theta

given the polar curve r = 2(1+cos theta) find the Cartesian
coordinates (x,y) of the point of the curve when theta = pi/2 and
find the slope of the tangent line to this polar curve at theta =
pi/2

Consider the polar curve r = 2 cos theta. Determine the slope of
the tangent line at theta = pi/4.

Find the area inside r = 2sin(3θ) and outside r = 1

Find the exact area of the region inside the circle
r=2cos(theta) but outside the circle r=1

Find the area of the region that lies INSIDE both curves
r=5cos(theta) and r = 2 + cos (theta)

1. Find the slope of the tangent line to r=2+sin30 at the point
where Θ=pi/4
2. Find the area of the region that lies inside the curve
r=4*sinΘ and outside the curve r=2

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