Difference between revisions of "009C Sample Final 2, Problem 7"

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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">a) Consider the function <math>f(x)=\bigg(1-\frac{1}{2}x\bigg)^{-2}.</math> Find the first three terms of its Binomial Series.
  
::<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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::<span class="exam">b) Find its radius of convergence.
 
 
::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
 
  
 
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Revision as of 11:23, 18 February 2017

a) Consider the function 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 f(x)=\bigg(1-\frac{1}{2}x\bigg)^{-2}.} Find the first three terms of its Binomial Series.
b) Find its radius of convergence.
Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

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

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