Difference between revisions of "009C Sample Final 1, Problem 1"

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<span class="exam">Compute
 
<span class="exam">Compute
  
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<span class="exam">a) <math>\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
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<span class="exam">(a) &nbsp; <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
  
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<span class="exam">b) <math>\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
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<span class="exam">(b) &nbsp; <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
  
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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<hr>
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!Foundations: &nbsp;
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[[009C Sample Final 1, Problem 1 Solution|'''<u>Solution</u>''']]
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|Review L'Hopital's Rule
 
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'''Solution:'''
 
  
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'''(a)'''
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[[009C Sample Final 1, Problem 1 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
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!Step 1: &nbsp;
 
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|First, we switch to the limit to <math>x</math> so that we can use L'Hopital's rule.
 
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|So, we have
 
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::<math>\begin{array}{rcl}
 
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\displaystyle{\lim_{x \rightarrow \infty}\frac{3-2x^2}{5x^2 + x +1}} & \overset{l'H}{=} & \displaystyle{\lim_{x \rightarrow \infty}\frac{-4x}{10x+1}}\\
 
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&&\\
 
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& \overset{l'H}{=} & \displaystyle{\frac{-4}{10}}\\
 
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&&\\
 
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& = & \displaystyle{\frac{-2}{5}}
 
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\end{array}</math>
 
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
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!Step 2: &nbsp;
 
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|-
 
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|Hence, we have
 
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|<math>\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}=\frac{-2}{5}</math>
 
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'''(b)'''
 
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!Step 1: &nbsp;
 
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
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!Step 2: &nbsp;
 
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!Step 3: &nbsp;
 
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
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!Final Answer: &nbsp;
 
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|'''(a)''' <math>\frac{-2}{5}</math>
 
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|'''(b)'''
 
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[[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]
 
[[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 17:55, 2 December 2017

Compute

(a)  

(b)  

Solution


Detailed Solution


Return to Sample Exam

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