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Practice Problems for 2/11

  1. Show that \(f(x)=\frac{x^2+3}{x+7}\) is continuous at the point \(x=1\).

  2. Come up with an example of a problem whose limit exists at \(x=8\), is defined at \(x=8\) but is not continuous at \(x=8\).

  3. Show that the equation \(\cos x=x\) has a solution between 0 and 1.