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

From Grad Wiki
Jump to navigation Jump to search
(Created page with "<span class="exam">Compute ::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math> ::<span class="exam">b) <mat...")
 
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;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"

Revision as of 12:01, 18 February 2017

A curve is given in polar coordinates by

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=1+\cos^2(2\theta)}
a) Show that the point with Cartesian coordinates Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (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
Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  
Final Answer:  
   (a)
   (b)

Return to Sample Exam

Retrieved from "https://gradwiki.math.ucr.edu/index.php?title=009C_Sample_Final_3,_Problem_7&oldid=2397"