Difference between revisions of "009C Sample Final 3, Problem 7"

Revision as of 12:01, 18 February 2017

A curve is given in polar coordinates by

r=1+\cos ^{2}(2\theta )

a) Show that the point with Cartesian coordinates

(x,y)={\bigg (}{\frac {\sqrt {2}}{2}},{\frac {\sqrt {2}}{2}}{\bigg )}

belongs to the curve.

b) Sketch the curve.

c) In Cartesian coordinates, find the equation of the tangent line at

{\bigg (}{\frac {\sqrt {2}}{2}},{\frac {\sqrt {2}}{2}}{\bigg )}.

Solution:

(a)

Step 2:

(b)

Step 2:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam">A curve is given in polar coordinates by
-::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
+::::::<math>r=1+\cos^2(2\theta)</math>
-::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
+::<span class="exam">a) Show that the point with Cartesian coordinates <math>(x,y)=\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg)</math> belongs to the curve.
+::<span class="exam">b) Sketch the curve.
+::<span class="exam">c) In Cartesian coordinates, find the equation of the tangent line at <math>\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg).</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"