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

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...")
 
 
(10 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
<span class="exam">Compute
+
<span class="exam">A curve is given in polar coordinates by
 +
::<span class="exam"><math>r=\sin(2\theta).</math>
  
−
::<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">(a) Sketch the curve.
  
−
::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
+
<span class="exam">(b) Compute &nbsp;<math style="vertical-align: -14px">y'=\frac{dy}{dx}.</math>
  
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+
<span class="exam">(c) Compute &nbsp;<math style="vertical-align: -14px">y''=\frac{d^2y}{dx^2}.</math>
−
!Foundations: &nbsp;
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|}
 
  
−
'''Solution:'''
+
<hr>
 +
[[009C Sample Final 2, Problem 9 Solution|'''<u>Solution</u>''']]
  
−
'''(a)'''
 
  
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+
[[009C Sample Final 2, Problem 9 Detailed Solution|'''<u>Detailed Solution</u>''']]
−
!Step 1: &nbsp;
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|}
 
  
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
−
!Step 2: &nbsp;
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|}
 
  
−
'''(b)'''
 
−
 
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
−
!Step 1: &nbsp;
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|}
 
−
 
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
−
!Step 2: &nbsp;
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|}
 
−
 
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
−
!Final Answer: &nbsp;
 
−
|-
 
−
|&nbsp;&nbsp; '''(a)'''
 
−
|-
 
−
|&nbsp;&nbsp; '''(b)'''
 
−
|}
 
 
[[009C_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]
 
[[009C_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 18:36, 2 December 2017

A curve is given in polar coordinates by

(a) Sketch the curve.

(b) Compute  

(c) Compute  

Solution


Detailed Solution


Return to Sample Exam

Retrieved from "https://gradwiki.math.ucr.edu/index.php?title=009C_Sample_Final_2,_Problem_9&oldid=4436"