Difference between revisions of "009A Sample Final 1, Problem 2"
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| − | + | <span class="exam"> Consider the following piecewise defined function: | |
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| − | + | ::<math>f(x) = \left\{ | |
| + | \begin{array}{lr} | ||
| + | x+5 & \text{if }x < 3\\ | ||
| + | 4\sqrt{x+1} & \text{if }x \geq 3 | ||
| + | \end{array} | ||
| + | \right. | ||
| + | </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 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:
- 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(x) = \left\{ \begin{array}{lr} x+5 & \text{if }x < 3\\ 4\sqrt{x+1} & \text{if }x \geq 3 \end{array} \right. }
(a) Show that 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(x)} is continuous at 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 x=3.}
(b) Using the limit definition of the derivative, and computing the limits from both sides, show that 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(x)} is differentiable at 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 x=3} .