009C Sample Final 2, Problem 9

A curve is given in polar coordinates by

$r=\sin(2\theta ).$

a) Sketch the curve.

b) Compute $y'={\frac {dy}{dx}}.$

c) Compute $y''={\frac {d^{2}y}{dx^{2}}}.$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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