Difference between revisions of "009A Sample Final 1, Problem 2"
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<span class="exam"> Consider the following piecewise defined function: | <span class="exam"> Consider the following piecewise defined function: | ||
| − | + | ::<math>f(x) = \left\{ | |
\begin{array}{lr} | \begin{array}{lr} | ||
x+5 & \text{if }x < 3\\ | x+5 & \text{if }x < 3\\ | ||
| Line 8: | Line 8: | ||
\right. | \right. | ||
</math> | </math> | ||
| − | <span class="exam">a) Show that <math>f(x)</math> is continuous at <math>x=3</math> | + | <span class="exam">(a) Show that <math style="vertical-align: -5px">f(x)</math> is continuous at <math style="vertical-align: 0px">x=3.</math> |
| − | <span class="exam">b) Using the limit definition of the derivative, and computing the limits from both sides, show that <math>f(x)</math> is differentiable at <math>x=3</math>. | + | <span class="exam">(b) Using the limit definition of the derivative, and computing the limits from both sides, show that <math style="vertical-align: -3px">f(x)</math> is differentiable at <math style="vertical-align: 0px">x=3</math>. |
| − | + | <hr> | |
| − | + | [[009A Sample Final 1, Problem 2 Solution|'''<u>Solution</u>''']] | |
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| − | ''' | + | [[009A Sample Final 1, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']] |
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[[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']] | [[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']] | ||
Latest revision as of 15:41, 2 December 2017
Consider the following piecewise defined function:
(a) Show that is continuous at
(b) Using the limit definition of the derivative, and computing the limits from both sides, show that is differentiable at .
