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Practice Problems for 2/4

  1. The height of a ball thrown into the air with velocity of 40 ft/s is given by \(h(t)=40t-16t^2\). Find the average velocity for the give time intervals:
    1. \([.5,1]\)
    2. \([1,2]\)
    3. Interpret the sign (positive or negative) of each of your answers.

  2. If \(f(x)=\frac{x^2-4}{x-2}\) and \(g(x)=x+2\),
    1. True or False: we can say that the functions \(f\) and \(g\) are equal. (Write one sentence justifying your response.)
    2. True or False: we can say that \(\lim_{x\rightarrow c}f(x)= \lim_{x\rightarrow c}g(x)\) for every real number \(c\). (Write one sentence justifying your response.)

  3. Find the value of the limit, or explain why the limit does not exist.
    4. $$\lim_{x\rightarrow 1}\frac{x^2+x+1}{x^3-1}$$