Difference between revisions of "009A Sample Final 3, Problem 4"

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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"> Discuss, without graphing, if the following function is continuous at <math>x=0.</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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::<math>f(x) = \left\{
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    \begin{array}{lr}
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      \frac{x}{|x|} &  \text{if }x < 0\\
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        0 &  \text{if }x = 0\\
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      x-\cos x & \text{if }x > 0
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    \end{array}
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  \right.
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</math>
  
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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">If you think <math>f</math> is not continuous at <math>x=0,</math> what kind of discontinuity is it?
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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>
 
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"

Revision as of 18:33, 17 February 2017

Discuss, without graphing, if the following function is continuous at

If you think 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 not continuous at what kind of discontinuity is it?

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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