Section 2.5

# Calculus reading for 2-27

If you look at the course calendar you will see that you need to read section 2.4 for Monday the 27th. I realize, however, that many of you still don’t have textbooks. Since I forgot to scan the section yesterday, I’ll give you an option. You can read section 2.4, or you can watch this video instead.

# Trigonometry Homework #3 due 3-2

Graph each function.

1. $\frac{1}{x+2}+2$

2. $\frac{-2}{x}-1$

3. $\frac{-1}{3x}$

4. $\frac{4}{-x}-4$

5. $\frac{1}{2x-5}-2$

# Calculus homework #2 due 2-16

1. Does $\lim_{x\rightarrow 1}\cot(\pi x)$ exist? Explain your answer.
2. Consider the graph of $f(x)$

State the value of each quantity, if it exists. If it does not exist, explain why.

$\lim_{x\rightarrow 0}f(x)$    $\lim_{x\rightarrow 0^{+}}f(x)$    $\lim_{x\rightarrow 2^{-}}f(x)$    $f(2)$    $\lim_{x\rightarrow 2}f(x)$

3. Sketch the graph of an example of a function $f(x)$ such that $\lim_{x\rightarrow 2}f(x)=3$, $\lim_{x\rightarrow -2}f(x)=0$, and $f(2)=f(-2)=1$.

4. Sketch the graph of an example of a function $f(x)$ such that $\lim_{x\rightarrow -1^{-}}f(x)=4$, $\lim_{x\rightarrow 1^{-}}f(x)=2$, and $f(x)$ is even.

# Trigonometry Homework #2 due 2-16

1. Find the unique polynomial $P(x)$ which satisfies the below list of conditions and write it in the form $P(x)=a_nx^n+\cdots+a_1x+a_0$.
• the degree is as small as possible
• the coefficients are real
• $P(4)=0$
• $P\left(\frac{-i}{3}\right)=0$
• $P(0)=1$
2. Sketch a graph of $f(x)=x^3-3x^2+4x-12$.
3. Re-write $x^5+x^4+x^3+x^2-12x-12$ as a product of linear factors.
4. Given $f(x)=ax^3-bx^2+3x+4$ and the graph of $f(x)$ below, find $a$ and $b$
5. Write the algebraic definition of the polynomial function graphed below.