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.

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 bucogydvo7k
  5. Write the algebraic definition of the polynomial function graphed below.6pd7zqmrch