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)

homework1

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.

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