Series Practice Problems for AP Calculus
Review the following concepts if needed:
- Sequences and Series for AP Calculus
- Types of Series: p-Series, Harmonic Series, Geometric Series, Decimal Expansion for AP Calculus
- Convergence Tests for AP Calculus
- Alternating Series for AP Calculus
- Power Series for AP Calculus
- Taylor Series and MacLaurin Series for AP Calculus
- Operations on Series for AP Calculus
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.
- Find the sum of the geometric series
- If the sum of the alternating series is approximated by s50, find the maximum absolute error.
- The Taylor series representation of ln x, centered at x =a.
- f(x )= ln x at x =e
- Estimate sin 9° accurate to three decimal places.
- Find the rational number equivalent to
- 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.
- Find the slope of the tangent line to the curve r =5 cos 3θ when θ =
- x3 ln xdx
Solutions for these practice problems can be found at: Solutions to Series Practice Problems for AP Calculus
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