Difference between revisions of "009C Sample Final 2, Problem 9"

Revision as of 18:16, 4 March 2017

A curve is given in polar coordinates by

r=\sin(2\theta ).

(a) Sketch the curve.

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

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

Solution:

(a)

ExpandStep 2:

(b)

ExpandStep 2:

(c)

ExpandStep 2:

@@ Line 4: / Line 4: @@
 <span class="exam">(a) Sketch the curve.
-<span class="exam">(b) Compute &nbsp;<math>y'=\frac{dy}{dx}.</math>
+<span class="exam">(b) Compute &nbsp;<math style="vertical-align: -14px">y'=\frac{dy}{dx}.</math>
-<span class="exam">(c) Compute &nbsp;<math>y''=\frac{d^2y}{dx^2}.</math>
+<span class="exam">(c) Compute &nbsp;<math style="vertical-align: -14px">y''=\frac{d^2y}{dx^2}.</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"