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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'''(c)'''
 
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!Step 2: &nbsp;
 
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!Final Answer: &nbsp;
 
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|'''(a)'''
 
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|'''(b)'''
 
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|'''(c)'''
 
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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    Hint:  

Solution


Detailed Solution


Return to Sample Exam

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