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

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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 curve is described parametrically by
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::::<span class="exam"><math>x=t^2</math>
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::::<span class="exam"><math>y=t^3-t</math>
  
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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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::<span class="exam">a) Sketch the curve for <math>-2\le t \le 2.</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">b) Find the equation of the tangent line to the curve at the origin.
  
 
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Revision as of 11:07, 18 February 2017

A curve is described parametrically by

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 x=t^2}
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 y=t^3-t}
a) Sketch the curve 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 -2\le t \le 2.}
b) Find the equation of the tangent line to the curve at the origin.
Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

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

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