Difference between revisions of "009A Sample Final 2, Problem 10"

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(Created page with "<span class="exam">Compute ::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math> ::<span class="exam">b) <math st...")
 
 
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<span class="exam">Compute
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<span class="exam">Let
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::<math>f(x)=\frac{4x}{x^2+1}</math>
  
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::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
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<span class="exam">(a) Find all local maximum and local minimum values of &nbsp;<math style="vertical-align: -4px">f,</math>&nbsp; find all intervals where &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is increasing and all intervals where &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is decreasing.
  
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::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
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<span class="exam">(b) Find all inflection points of the function &nbsp;<math style="vertical-align: -4px">f,</math>&nbsp; find all intervals where the function &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is concave upward and all intervals where &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is concave downward.
  
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::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
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<span class="exam">(c) Find all horizontal asymptotes of the graph &nbsp;<math style="vertical-align: -5px">y=f(x).</math>
  
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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<span class="exam">(d) Sketch the graph of &nbsp;<math style="vertical-align: -5px">y=f(x).</math>
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!Foundations: &nbsp;
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[[009A Sample Final 2, Problem 10 Solution|'''<u>Solution</u>''']]
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[[009A Sample Final 2, Problem 10 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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!Final Answer: &nbsp;
 
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[[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 10:29, 1 December 2017

Let

(a) Find all local maximum and local minimum values of    find all intervals where    is increasing and all intervals where    is decreasing.

(b) Find all inflection points of the function    find all intervals where the function    is concave upward and all intervals where    is concave downward.

(c) Find all horizontal asymptotes of the graph  

(d) Sketch the graph of  

Solution


Detailed Solution


Return to Sample Exam

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