Series Practice Problems for AP Calculus

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By — McGraw-Hill Professional
Updated on Aug 29, 2014

Review the following concepts if needed:

Determine whether each series converges or diverges.

Find the interval of convergence for each series.

Approximate each function with a fourth degree Taylor polynomial centered at the given value of x.

Find the MacLaurin series for each function and determine its interval of convergence.

  1. Find the sum of the geometric series
  2. If the sum of the alternating series is approximated by s50, find the maximum absolute error.
  3. The Taylor series representation of ln x, centered at x =a.
  4. f(x )= ln x at x =e
  5. Estimate sin 9° accurate to three decimal places.
  6. Find the rational number equivalent to


  1. The movement of an object in the plane is defined by x (t)= ln t, y (t)=t2. Find the speed of the object at the moment when the acceleration is a(t)= −1, 2.
  2. Find the slope of the tangent line to the curve r =5 cos 3θ when θ =
  3. x3 ln xdx

Solutions for these practice problems can be found at: Solutions to Series Practice Problems for AP Calculus

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