Difference between revisions of "009A Sample Final 3, Problem 10"

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<span class="exam">Let <math>y=\tan(x).</math>
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<span class="exam">Let &nbsp;<math style="vertical-align: -5px">y=\tan(x).</math>
  
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<span class="exam">(a) Find the differential <math>dy</math> of <math>y=\tan (x)</math> at <math>x=\frac{\pi}{4}.</math>  
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<span class="exam">(a) Find the differential &nbsp;<math style="vertical-align: -4px">dy</math>&nbsp; of &nbsp;<math style="vertical-align: -5px">y=\tan (x)</math>&nbsp; at &nbsp;<math style="vertical-align: -15px">x=\frac{\pi}{4}.</math>  
  
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<span class="exam">(b) Use differentials to find an approximate value for <math>\tan(0.885).</math> Hint: <math>\frac{\pi}{4}\approx 0.785.</math>
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<span class="exam">(b) Use differentials to find an approximate value for &nbsp;<math style="vertical-align: -5px">\tan(0.885).</math>&nbsp; Hint: &nbsp;<math style="vertical-align: -15px">\frac{\pi}{4}\approx 0.785.</math>
  
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!Foundations: &nbsp;
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[[009A Sample Final 3, Problem 10 Solution|'''<u>Solution</u>''']]
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|What is the differential  &nbsp;<math style="vertical-align: -4px">dy</math>&nbsp; of &nbsp;<math style="vertical-align: -4px">y=x^2</math>&nbsp; at &nbsp;<math style="vertical-align: -1px">x=1?</math>
 
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&nbsp; &nbsp; &nbsp; &nbsp; Since &nbsp;<math style="vertical-align: -4px">x=1,</math>&nbsp; the differential is &nbsp;<math style="vertical-align: -4px">dy=2xdx=2dx.</math>
 
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'''Solution:'''
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[[009A Sample Final 3, Problem 10 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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'''(a)'''
 
  
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!Step 1: &nbsp;
 
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|First, we find the differential &nbsp;<math style="vertical-align: -4px">dy.</math>
 
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|Since &nbsp;<math style="vertical-align: -5px">y=\tan x,</math>&nbsp; we have
 
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&nbsp; &nbsp; &nbsp; &nbsp;<math>dy\,=\,\sec^2 x\,dx.</math>
 
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!Step 2: &nbsp;
 
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|Now, we plug &nbsp;<math style="vertical-align: -15px">x=\frac{\pi}{4}</math>&nbsp; into the differential from Step 1.
 
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|So, we get
 
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&nbsp; &nbsp; &nbsp; &nbsp;<math>dy\,=\,\bigg(\sec\bigg(\frac{\pi}{4}\bigg)\bigg)^2\,dx\,=\,2\,dx.</math>
 
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'''(b)'''
 
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!Step 2: &nbsp;
 
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'''(c)'''
 
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!Final Answer: &nbsp;
 
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|'''(a)'''
 
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[[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 16:49, 2 December 2017

Let  

(a) Find the differential    of    at  

(b) Use differentials to find an approximate value for  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 \tan(0.885).}   Hint:  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 \frac{\pi}{4}\approx 0.785.}

Solution


Detailed Solution


Return to Sample Exam

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