Question

Consider the polar curve r =1 + 2 cos(theta). Find dy dx at theta = 3 .

Answer #1

Given the polar curve: r = cos(theta) - sin(theta)
Find dy/dx

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

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

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 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

Consider the polar curve ? = cos(?) + 1. To find the area
enclosed by the curve, a student computes: A = ∫ 1/2(???2? + 2????
+ 1)??. bounds (0,pi) Explain the mistake.

Find the area that lies simultaneously outside the polar curve r
= cos θ and inside the polar curve r = 1 + cos θ.

Find the length of the polar curve r = e^-theta, o lesser or
equal to theta lesser or equal to 3pi. Please write as large and
neatly as possible. Thank you.

cos(xy) = 1 + sin4y
find dy/dx

If R(theta)=[(cos, -sin)
(sin, cos)]
1) show that R(theta) is a linear transformation from
R2->R2
2)Show that R(theta) of R(alpha) = R(theta + alpha)
3) Find R(45degrees) [(x),
(y)], interpret it geometrically

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