009C Sample Final 1, Problem 7

A curve is given in polar coordinates by

$r=1+\sin \theta$

a) Sketch the curve.

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

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

ExpandFoundations:

Solution:

(a)

ExpandStep 1:
Insert sketch of graph

(b)

ExpandStep 1:

ExpandStep 2:

ExpandStep 3:

(c)

ExpandStep 1:

ExpandStep 2:

ExpandFinal Answer:
(a)
(b)
(c)

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