Difference between revisions of "009B Sample Final 2, Problem 5"

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(Created page with "<span class="exam">Consider the region bounded by the following two functions: ::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math styl...")
 
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<span class="exam">Consider the region bounded by the following two functions:
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::<span class="exam">a) Find the area of the surface obtained by rotating the arc of the curve
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::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
 
  
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<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
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::::<math>y^3=x</math>
  
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<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.  
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::<span class="exam">between <math>(0,0)</math> and <math>(1,1)</math> about the <math>y</math>-axis.
  
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<span class="exam">c) Find the actual area of the region.
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::<span class="exam">b) Find the length of the arc
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::::<math>y=1+9x^{\frac{3}{2}}</math>
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::<span class="exam">between the points <math>(1,10)</math> and <math>(4,73).</math>
  
 
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"

Revision as of 19:19, 17 February 2017

a) Find the area of the surface obtained by rotating the arc of the curve
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 y^3=x}
between 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 (0,0)} and 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 (1,1)} about the 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 y} -axis.
b) Find the length of the arc
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 y=1+9x^{\frac{3}{2}}}
between the points 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 (1,10)} and 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 (4,73).}
Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  

(c)

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

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