---
# System prepended metadata

title: 微積分小考
tags: [微積分]

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---
title: 微積分小考
tags: 微積分
description: View the slide with "Slide Mode".
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## 10/7微積分小考 企管 
學號: 
姓名:
### 1. Find the domain of the given functions:

- 1. $f(x)=x^2+3$
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- 2. $f(x)=\frac{3x+1}{x^2}$
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- 3. $f(x)=\sqrt{5-x}$
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- 4. $f(x)=\frac{\sqrt{x-1}}{(x+2)(x-3)}$
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### 2.  Patricia wishes to have a retangular garden in her backyard. She has 80m of fencing with which to enclose her garden. Letting $x$ denote the width of the garden, find: 1. the function $f$ in the variable $x$ giving the area of the garden, and 2. the domain of $x$?
![](https://i.imgur.com/utBWoab.png =25%x)
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### 3. Let $f(x)=\frac{x^2}{x^2+1}$, show:
&#160;&#160;a.    $f(x)$ is nonnegative for all values of $x$.
&#160;&#160;b.    $f$ is continuous for all values of $x$.
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### 4. Show the function: $f(x)=|x-4|$ does not have a derivative at $x=4.$
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### 5. Let 
$$   g(x) = \left\{\begin{array}{ll}
                 x^2-4x+8, & \mbox{if $x\le-2$} \\
                 ax+b, & \mbox{if $x>-2$} 
                \end{array} \right.
$$
#### &#160;&#160;&#160;&#160;&#160;Find the values of $a$ and $b$ such that $f$ is continuous and has a derivative at $x=-2$.