Chapter 1: Problem 37
Determine whether the points are collinear. (Three points are collinear if they lie on the same line.) $$ (-2,1),(-1,0),(2,-2) $$
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Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If the inverse function of \(f\) exists, then the \(y\) -intercept of \(f\) is an \(x\) -intercept of \(f^{-1}\).
Determine all polynomials \(P(x)\) such that $$ P\left(x^{2}+1\right)=(P(x))^{2}+1 \text { and } P(0)=0 . $$
Find two functions \(f\) and \(g\) such that \(\lim _{x \rightarrow 0} f(x)\) and \(\lim _{x \rightarrow 0} g(x)\) do not exist, but \(\lim _{x \rightarrow 0}[f(x)+g(x)]\) does exist.
Use a graphing utility to graph \(f(x)=\sin x \quad\) and \(\quad g(x)=\arcsin (\sin x)\) Why isn't the graph of \(g\) the line \(y=x ?\)
A dial-direct long distance call between two cities costs \(\$ 1.04\) for the first 2 minutes and \(\$ 0.36\) for each additional minute or fraction thereof. Use the greatest integer function to write the cost \(C\) of a call in terms of time \(t\) (in minutes). Sketch the graph of this function and discuss its continuity.
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