MTH 132 Section Objectives

Steve Kifowit, Waubonsee Community College
Section 2.1
  1. Find the area of a bounded region between the graphs of two functions.
Section 2.2
  1. Use disks or washers to find the volume of a solid of revolution.
  2. Find the volume of a solid with known cross sections.
Section 2.3
  1. Use cylindrical shells to find the volume of a solid of revolution.
Section 2.4
  1. Find the length of a smooth curve in the plane.
  2. Find the surface area of a solid of revolution.
Section 2.5
  1. Compute the work done by a variable force acting along a horizontal or vertical line.
  2. Compute the force of a fluid on a submerged vertical plate.
Section 2.6
  1. Compute the mass and center of mass of a one-dimensional (linear) object.
  2. Compute the mass and center of mass of a two-dimensional (planar) object.
Section 2.9
  1. Define the hyperbolic functions in terms of the exponential function.
  2. Derive and apply the formulas for derivatives and integrals of the hyperbolic functions.
  3. Become acquainted with the formulas for the derivatives of the inverse hyperbolic functions and their associated integrals.
Section 3.1
  1. Recognize when to use integration by parts.
  2. Use integration by parts to evaluate indefinite and definite integrals.
Section 3.2
  1. Evaluate integrals involving products and powers of sines and cosines.
  2. Evaluate integrals involving products and powers of secants and tangents.
  3. Use trigonometric identities when evaluating integrals.
Section 3.3
  1. Use trigonometric substitutions to evaluate indefinite and definite integrals.
Section 3.4
  1. Compute the partial fraction decomposition of a rational expression.
  2. Integrate rational functions by using partial fractions.
Section 3.6
  1. Use the trapezoid rule to approximate definite integrals.
Section 3.7
  1. Recognize improper integrals and determine why an integral is improper.
  2. Evaluate improper integrals defined on unbounded intervals.
  3. Evaluate improper integrals whose integrands have infinite discontinuities.
Section 5.1
  1. Find the terms of a sequence.
  2. Determine whether a sequence converges or diverges.
  3. Find the limit of a convergent sequence.
Section 5.2
  1. Explain the meaning of an infinite series, its partial sums, and its convergence or divergence.
  2. Determine whether a geometric series converges or diverges. If possible, find its sum.
  3. Recognize telescoping series, and determine convergence or divergence.
Section 5.3
  1. Apply the -th term test for divergence. (The test cannot be used for convergence.)
  2. Apply the integral test to determine convergence or divergence of a series.
  3. Recognize a -series and determine whether it converges or diverges.
Section 5.4
  1. Use direct comparison to determine whether a series converges or diverges.
  2. Use limit comparison to determine whether a series converges or diverges.
Section 5.5
  1. Recognize alternating series and use the alternating series test.
  2. Determine when a series is absolutely or conditionally convergent.
  3. Estimate the sum of an alternating series.
Section 5.6
  1. Use the ratio test to determine absolute convergence of a series.
  2. Use the root test to determine absolute convergence of a series.
Section 6.1
  1. Recognize and identify power series.
  2. Determine the radius and interval of convergence of a power series.
  3. Use power series to represent functions
Section 6.2
  1. Combine power series by using algebraic operations.
  2. Differentiate and integrate power series term-by-term.
Section 6.3
  1. Find the Taylor polynomial for a function.
  2. Use Taylor's theorem to estimate the error made in approximating a function by its Taylor polynomial.
  3. Find the Taylor series for a function.
  4. Recognize when a Taylor series converges to its function.
Section 7.1
  1. Sketch the graph of a set of parametric equations.
  2. Find a set of parametric equations for a function/curve.
  3. Eliminate the parameter from a set of parametric equations.
Section 7.2
  1. Determine derivatives for parametric curves.
  2. Find the arc length of a parametric curve.
  3. Find the area between a parametric curve and the horizontal axis.
Section 7.3
  1. Locate points in the plane by using polar coordinates.
  2. Convert points and equations between rectangular and polar coordinates.
  3. Sketch polar curves.
Section 7.4
  1. Find the arc length of a polar curve.
  2. Find the area of a polar region.

Last updated August 15, 2022

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