Calculus II

  1. Inverse Trigonometric Functions: I can
    • differentiate the inverse trigonometric functions,
    • use inverse trigonometric functions to evaluate integrals.
  2. L'Hôpital's Rule: I can
    • identify the indeterminate forms,
    • evaluate limits involving indeterminate forms.
  3. Area and Volumes: I can
    • compute the area bounded by two curves,
    • find the volume of a solid obtained by revolving a region around an axis.
  4. Integration by Parts: I can
    • identify when it is appropriate to use the method of integration by parts to evaluate an integral,
    • evaluate integrals using the method of integration by parts.
  5. Partial Fraction Decomposition: I can
    • identify the types of partial fraction decompositions,
    • decompose a rational function,
    • integrate rational functions.
  6. Approximate Integration: I can
    • approximate the value of a definite integral using the Trapezoidal Rule,
    • approximate the value of a definite integral using Simpson's Rule,
    • approximate the value of a definite integral using the Midpoint rule,
    • estimate the error associated with each rule.
  7. Improper Integrals: I can
    • evaluate improper integrals of Type 1,
    • evaluate improper integrals of Type 2,
    • use the Comparison Test to decide whether an improper integral converges.
  8. Differential Equations: I can
    • identify whether a given function is a solution to a differential equation,
    • solve initial value problems by the method of Separation of Variables.
  9. Parametric Equations: I can
    • parameterize a curve in the plane,
    • find the line tangent to a point on a parametric curve.
  10. Polar Coordinates: I can
    • sketch polar curves,
    • find the line tangent to a polar curve at a given point.
  11. Sequences: I can
    • find the general term of a sequence from a given pattern,
    • determine whether a sequence is increasing or decreasing,
    • determine whether a function is bounded above or below,
    • use the Monotonic Sequence Theorem to determine if a given sequence converges,
    • find the limit of a sequence.
  12. Geometric Series: I can
    • find the general term of a geometric series,
    • determine whether a geometric series is convergent and, if so, find its sum.
  13. The Integral Test: I can
    • find a function that agrees with the terms of a series on the positive integers,
    • use an improper integral to determine whether a series converges,
    • use the Remainder Estimate to bound the sum of a series.
  14. Comparison Tests: I can
    • use the Comparison Test to determine whether a series converges,
    • use the Limit Comparison Test to determine whether a series converges.
  15. Alternating Series: I can
    • determine whether an alternating series converges,
    • estimate the sum of an alternating series.
  16. Ratio and Root Tests: I can
    • use the ratio test to determine whether a series is absolutely convergent,
    • use the root test to determine whether a series is absolutely convergent,
    • determine whether a series is conditionally convergent.
  17. Power Series: I can
    • determine the radius of convergence for a power series,
    • determine the interval of convergence for a power series.
  18. Taylor Series: I can
    • compute the Taylor expansion for a function,
    • use Taylor's Inequality to estimate the remainder of a Taylor series,
    • show that a function is equal to its Taylor expansion on its interval of convergence.