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

Text for This Topic
Index of On-Line Topics
Everything for Calculus
Everything for Finite Math
Everything for Finite Math & Calculus
Utility: Function Evaluator & Grapher
Español 1. Let $f$ have the graph shown below. $f$ is Select one continuous discontinuous undefined at $x = -2$ $f$ is Select one continuous discontinuous undefined at $x = -1$ $f$ is Select one continuous discontinuous undefined at $x = 0$ $f$ is Select one continuous discontinuous undefined at $x = 1$ $f$ is Select one continuous discontinuous undefined at $x = 2$ $f$ is Select one continuous discontinuous undefined at $x = 3$ 2. Let $f$ be specified by
$f(x) =$ $x$ if $x < -1$ $\frac{x}{x + 1}$ if $-1 < x ≤ 1$ $\frac{x}{2}$ if $1 < x ≤ 2$ $x$ if $x > 2$
.
 $f$ is Select one continuous discontinuous undefined at $x = -2$ $f$ is Select one continuous discontinuous undefined at $x = -1$ $f$ is Select one continuous discontinuous undefined at $x = 0$ $f$ is Select one continuous discontinuous undefined at $x = 1$ $f$ is Select one continuous discontinuous undefined at $x = 2$ $f$ is Select one continuous discontinuous undefined at $x = 3$ 3. Find the values of $h$ and $k$ that make the following function $g$ continuous.
$g(x) =$ $x^2 + h$ if $x < -1$ $x + 4$ if $-1 < x ≤ 1$ $\frac{x}{x + k}$ if $x > 1$
.
 $h =$ $k =$ 4. Here are some multiple choice questions.

(a)
 If $f$ is continuous at the point $x = a,$ then $lim$$x→a^{-} f(x) is Select one always not always never equal to f(a). (b)  If f is not continuous at the point x = a, then lim$$x→a^{-}$ $f(x)$ Select one must may or may not cannot exist. (c)
 If $f$ is not continuous at the point $x = a,$ then $f'(a)$ Select one must may or may not cannot exist. (d)
 If $f$ is not differentiable at the point $x = a,$ then $f$ Select one must may or may not cannot be continuous at $x = a.$ 5. Let $f$ have the graph shown below. $f$ is Select one differentiable discontinuous continuous but not differentiable undefined at $x = -2$ $f$ is Select one differentiable discontinuous continuous but not differentiable undefined at $x = -1$ $f$ is Select one differentiable discontinuous continuous but not differentiable undefined at $x = 0$ $f$ is Select one differentiable discontinuous continuous but not differentiable undefined at $x = 1$ $f$ is Select one differentiable discontinuous continuous but not differentiable undefined at $x = 2$ $f$ is Select one differentiable discontinuous continuous but not differentiable undefined at $x = 3$ 6. Make the appropriate choices below.

 $f(x) = (x+1)^{1/3}(x-2)^{4/3}$ is Select one not differentiable differentiable undefined at $x = -1$ $f(x) = (x+1)^{1/3}(x-2)^{4/3}$ is Select one not differentiable differentiable undefined at $x = 2$ $f(x) = (x+1)^{2/3}(x-2)^{-1}$ is Select one not differentiable differentiable undefined at $x = -1$ $f(x) = (x+1)^{2/3}(x-2)^{-1}$ is Select one not differentiable differentiable undefined at $x = 2$ $f(x) = \|x+1\| \|x-2|^2$ is Select one not differentiable differentiable undefined at $x = -1$ $f(x) = \|x+1\| \|x-2|^2$ is Select one not differentiable differentiable undefined at $x = 2$   Last Updated:October, 1999
Copyright © 1999 StefanWaner and Steven R. Costenoble