Difference between revisions of "009C Sample Final 3, Problem 5"

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(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...")
 
 
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<span class="exam">Compute
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<span class="exam"> Consider the function
  
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::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
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::<math>f(x)=e^{-\frac{1}{3}x}.</math>
  
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::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
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<span class="exam">(a) Find a formula for the &nbsp;<math>n</math>th derivative &nbsp;<math style="vertical-align: -5px">f^{(n)}(x)</math>&nbsp; of &nbsp;<math style="vertical-align: -5px">f</math>&nbsp; and then find &nbsp;<math style="vertical-align: -5px">f'(3).</math>
  
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<span class="exam">(b) Find the Taylor series for &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; at &nbsp;<math style="vertical-align: -5px">x_0=3,</math>&nbsp; i.e. write &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; in the form
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!Foundations: &nbsp;  
 
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'''Solution:'''
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::<math>f(x)=\sum_{n=0}^\infty a_n(x-3)^n.</math>
  
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'''(a)'''
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[[009C Sample Final 3, Problem 5 Solution|'''<u>Solution</u>''']]
  
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!Step 1: &nbsp;
 
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[[009C Sample Final 3, Problem 5 Detailed Solution|'''<u>Detailed Solution</u>''']]
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!Step 2: &nbsp;
 
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'''(b)'''
 
  
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!Step 1: &nbsp;
 
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!Final Answer: &nbsp;
 
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|&nbsp;&nbsp; '''(a)'''
 
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|&nbsp;&nbsp; '''(b)'''
 
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[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]
 
[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 16:20, 3 December 2017

Consider the function

(a) Find a formula for the  th derivative    of    and then find  

(b) Find the Taylor series for    at    i.e. write    in the form

Solution


Detailed Solution


Return to Sample Exam

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