Question

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.

Answer #1

length of polar curve is given by

Find the arc length (exact value) of the polar curve r = 2sintheta
+ 4 costheta.
0 <= theta <= 3pi/4 by setting up and evaluating a
definite integral.

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

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

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 length of the parabolic segment r = 6/(1+cos theta), 0
less than or equal to theta less than or equal to pi/2. Please show
a graph. If you could, please write legibly and indicate why each
step was taken. It is a great help!

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

find the length of the polar curve r=sin^2x. use symmetry and
consider only 0 to pie/2

2)Find the slope of the tangent line to the curve r = sin (O) +
cos (O) at O = pi / 4 (O means theta)
3)Find the unit tangent vector at t = 0 for the curve r (t) =
4sen (t) i + 3tj + cos (t) k
4)A uniform cable measuring 40 feet is hung from the top of a
building. The cable weighs 60 pounds. How much work in foot-pounds
is required to climb 10 feet...

Sketch the curve with the given polar equation by first
sketching the graph of r as a function of θ in Cartesian
coordinates.
r=3sin2θ
and
r= cos3θ
and
r= 4cos(2θ)
Please show symmetry tests
Thank you in advance!

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

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