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Practice Problems for 2/6

  1. Evaluate the limit and justify each step by citing the appropriate Limit Laws. \[ \lim_{t\rightarrow 2}(t+1)^9(\sqrt{t^2-1}). \]

  2. If all you know is that \(3x \leq f(x) \leq x^3+x^2+1\) for all \(x\), what can you say about \(\lim_{x\rightarrow 1} f(x)\)?

  3. Find \( \lim_{x\rightarrow 0}\frac{|x|}{x}\) or show the limit does not exist.