---
title: 微積分小考
tags: 微積分
description: View the slide with "Slide Mode".
---

## 10/7微積分小考 企管
學號:
姓名:
### 1. Find the domain of the given functions:

- 1. $f(x)=x^2+3$
 
- 2. $f(x)=\frac{3x+1}{x^2}$
 
- 3. $f(x)=\sqrt{5-x}$
 
- 4. $f(x)=\frac{\sqrt{x-1}}{(x+2)(x-3)}$
 
 

### 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 $x$?
 
 
 

### 3. Let $f(x)=\frac{x^2}{x^2+1}$, show:
  a. $f(x)$ is nonnegative for all values of $x$.
  b. $f$ is continuous for all values of $x$.
 
 
 
 
 
### 4. Show the function: $f(x)=|x-4|$ does not have a derivative at $x=4.$
 
 
 
 
 
### 5. Let
$$ g(x) = \left\{\begin{array}{ll}
x^2-4x+8, & \mbox{if $x\le-2$} \\
ax+b, & \mbox{if $x>-2$}
\end{array} \right.
$$
####      Find the values of $a$ and $b$ such that $f$ is continuous and has a derivative at $x=-2$.