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Practice Problems for 2/25

  1. Consider the function \(f(x)=\sqrt[3]{x}\)
    1. Show that \(f\) is continuous at the point \(x=0\).
    2. Use the limit definition of a derivative to determine whether or not \(f(x)\) is differentiable at \(x=0\).
    3. What does the graph of the function look like in a small interval around \(x=0\)?

  2. Find the derivative of \(f(x)= 2x^{-2/5}+\frac{x^5+3x^2+4}{x^{11}+9x^7}+5\)