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

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<span class="exam">A curve is given in polar coordinates by  
 
<span class="exam">A curve is given in polar coordinates by  
  
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::::::<math>r=1+\cos^2(2\theta)</math>
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::<math>r=1+\cos^2(2\theta)</math>
  
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::<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.
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<span class="exam">(a) Show that the point with Cartesian coordinates &nbsp;<math>(x,y)=\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg)</math>&nbsp; belongs to the curve.
  
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::<span class="exam">b) Sketch the curve.  
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<span class="exam">(b) Sketch the curve.  
  
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::<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>
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<span class="exam">(c) In Cartesian coordinates, find the equation of the tangent line at &nbsp;<math>\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg).</math>
  
 
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'''Solution:'''
 
'''Solution:'''
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'''(c)'''
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!Step 1: &nbsp;
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!Step 2: &nbsp;
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|&nbsp;&nbsp; '''(b)'''  
 
|&nbsp;&nbsp; '''(b)'''  
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|&nbsp;&nbsp; '''(c)'''
 
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[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]
 
[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Revision as of 17:59, 4 March 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  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 \bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg).}

Foundations:  


Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  

(c)

Step 1:  
Step 2:  


Final Answer:  
   (a)
   (b)
   (c)

Return to Sample Exam

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