1. Consider the function f de?ned by
![2194_Limit de?nition of horizontal asymptote.png](https://secure.expertsmind.com/CMSImages/2194_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote.png)
The ?rst and second derivatives of f are
![776_Limit de?nition of horizontal asymptote1.png](https://secure.expertsmind.com/CMSImages/776_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote1.png)
(a) Determine the domain of f . Write your answer in interval notation.
(b) What are the x-intercept(s) of the graph of f ? What are the y-intercept(s) of the graph of f ?
![1931_Limit de?nition of horizontal asymptote2.png](https://secure.expertsmind.com/CMSImages/1931_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote2.png)
(c) Find each horizontal asymptote of the graph of f , if any exists, by using the limit de?nition of horizontal asymptote.
(d) Find each vertical asymptote of the graph of f , if any exists, by using the limit de?nition of vertical asymptote.
![235_Limit de?nition of horizontal asymptote3.png](https://secure.expertsmind.com/CMSImages/235_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote3.png)
(e) Find where f is increasing, and where f is decreasing? Write your answer in interval notation.
(f) Find critical points of f and classify each as a local maximum, a local minimum, or neither.
![1999_Limit de?nition of horizontal asymptote4.png](https://secure.expertsmind.com/CMSImages/1999_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote4.png)
(g) Determine where the graph of f concave up, and where the graph of f concave down? Write your answer in interval notation.
(h) sketch the graph f.
![695_Limit de?nition of horizontal asymptote5.png](https://secure.expertsmind.com/CMSImages/695_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote5.png)
2. (a) Find the linearization of f (x) = (x + 1)4 at a = 1, and use it to approximate (2.01)4
(b) Evaluate
dx by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and ?nd the area using high school geometry.
3. Evaluate the following limits using L'Hospital's Rule.
![830_Limit de?nition of horizontal asymptote7.png](https://secure.expertsmind.com/CMSImages/830_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote7.png)
![864_Limit de?nition of horizontal asymptote8.png](https://secure.expertsmind.com/CMSImages/864_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote8.png)
![656_Limit de?nition of horizontal asymptote9.png](https://secure.expertsmind.com/CMSImages/656_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote9.png)
4. Dierentiate the following functions.
![1871_Limit de?nition of horizontal asymptote10.png](https://secure.expertsmind.com/CMSImages/1871_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote10.png)
![2077_Limit de?nition of horizontal asymptote11.png](https://secure.expertsmind.com/CMSImages/2077_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote11.png)
![705_Limit de?nition of horizontal asymptote12.png](https://secure.expertsmind.com/CMSImages/705_Limit%20de%EF%AC%81nition%20of%20horizontal%20asymptote12.png)
5. Evaluate the following de?nite integrals.
![1942_Determine the domain1.png](https://secure.expertsmind.com/CMSImages/1942_Determine%20the%20domain1.png)
6. A farmer wants to fence o a rectangular ?eld and then divide the ?eld in half with a fence down the middle (see diagram below). If he can only aord 240 ft. of fencing material, what is the width y which gives the maximum area of the ?eld?
![221_Determine the domain2.png](https://secure.expertsmind.com/CMSImages/221_Determine%20the%20domain2.png)