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

Latest revision as of 16:38, 2 December 2017

Discuss, without graphing, if the following function is continuous at $x=0.$

f(x)=\left\{{\begin{array}{lr}{\frac {x}{|x|}}&{\text{if }}x<0\\0&{\text{if }}x=0\\x-\cos x&{\text{if }}x>0\end{array}}\right.

If you think $f$ is not continuous at $x=0,$ what kind of discontinuity is it?

@@ Line 11: / Line 11: @@
 <span class="exam">If you think &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is not continuous at &nbsp;<math style="vertical-align: -4px">x=0,</math>&nbsp; what kind of discontinuity is it?
+<hr>
+[[009A Sample Final 3, Problem 4 Solution|'''<u>Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Foundations: &nbsp;
-|-
-|<math style="vertical-align: -5px">f(x)</math>&nbsp; is continuous at &nbsp;<math style="vertical-align: 0px">x=a</math>&nbsp; if
-|-
-|&nbsp; &nbsp; &nbsp; &nbsp;<math style="vertical-align: -14px">\lim_{x\rightarrow a^+}f(x)=\lim_{x\rightarrow a^-}f(x)=f(a).</math>
-|}
+[[009A Sample Final 3, Problem 4 Detailed Solution|'''<u>Detailed Solution</u>''']]
-'''Solution:'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
-|-
-|
-|-
-|
-|-
-|
-|-
-|
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
-|-
-|
-|-
-|
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
-|-
-|
-|}
 [[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]