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 <math>f,</math> find all intervals where <math>f</math> is increasing and all intervals where <math>f</math> 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 <math>f,</math> find all intervals where the function <math>f</math> is concave upward and all intervals where <math>f</math> 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 <math>y=f(x).</math>
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::<span class="exam">d) Sketch the graph of <math>y=f(x).</math>
  
 
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Revision as of 18:30, 17 February 2017

Let

a) Find all local maximum and local minimum values of find all intervals where 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} is increasing and all intervals where 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} is decreasing.
b) Find all inflection points of 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,} find all intervals where 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} is concave upward and all intervals where 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} is concave downward.
c) Find all horizontal asymptotes of the graph 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=f(x).}
d) Sketch the graph of 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=f(x).}
Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  

(c)

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

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