Continuity & Differentiability
miscellaneous on-line topics for
Calculus Applied to the Real World
Exercises

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1. Let $f$ have the graph shown below.
$f$ is at $x = -2$     $f$ is at $x = -1$
$f$ is at $x = 0$     $f$ is at $x = 1$
$f$ is at $x = 2$       $f$ is at $x = 3$

2. Let $f$ be specified by
$f$ is at $x = -2$     $f$ is at $x = -1$
$f$ is at $x = 0$     $f$ is at $x = 1$
$f$ is at $x = 2$       $f$ is at $x = 3$

3. Find the values of $h$ and $k$ that make the following function $g$ continuous.
$h =$       $k =$

4. Here are some multiple choice questions.

(a)
If $f$ is continuous at the point $x = a,$ then $lim$
$x→a^{-}$		 $f(x)$is equal to $f(a).$  
(b)
If $f$ is not continuous at the point $x = a,$ then $lim$
$x→a^{-}$		 $f(x)$ exist.  
(c)
If $f$ is not continuous at the point $x = a,$ then $f'(a)$ exist.  
(d)
If $f$ is not differentiable at the point $x = a,$ then $f$ be continuous at $x = a.$  

5. Let $f$ have the graph shown below.
$f$ is at $x = -2$
$f$ is at $x = -1$
$f$ is at $x = 0$
$f$ is at $x = 1$
$f$ is at $x = 2$
$f$ is at $x = 3$

6. Make the appropriate choices below.

$f(x) = (x+1)^{1/3}(x-2)^{4/3}$ is at $x = -1$
$f(x) = (x+1)^{1/3}(x-2)^{4/3}$ is at $x = 2$
$f(x) = (x+1)^{2/3}(x-2)^{-1}$ is at $x = -1$
$f(x) = (x+1)^{2/3}(x-2)^{-1}$ is at $x = 2$
$f(x) = \|x+1\| \|x-2|^2$ is at $x = -1$
$f(x) = \|x+1\| \|x-2|^2$ is at $x = 2$

 

Return to Main Page
Text for This Topic
Index of On-Line Topics
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Utility: Function Evaluator & Grapher

Last Updated:October, 1999
Copyright © 1999 StefanWaner and Steven R. Costenoble