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Instructions

The goal of this quiz is for you to demonstrate as many of the Learning Outcomes as possible (see the bottom of the sheet) by finding out anything you can about the information below. Notice that there is no question—you need to supply that. I am providing you with a Sage cell in case that is useful.

To get credit for a Learning Outcome, you must demonstrate it correctly, put a label (e.g. S3) on the left side of your sheet, and draw an error from the label to exactly where you demonstrate it in your work. Your goal is to make sure that I know that you know where you are demonstrating the Learning Outcome. See the sample Quizzes on Canvas if you have questions. Make a special effort to incorporate the five CORE outcomes.

Do your work on a separate sheet of paper, and then upload a picture (or type your work into Canvas using the Math Menu) into Canvas.

The Information

\begin{equation*} f(x)=x^2e^x \end{equation*}

Sage Cell (use only if you need it)

Learning Outcomes

Group I: I can use integrals to solve authentic real-life application problems.

  • I1: I can solve separable differential equations.
  • I2: I can compute integrals using integration by parts.
  • I3 (CORE): I can solve real-world problems by slicing and integrating.
  • I4: I can compute improper integrals.
  • I5: I evaluate a double integral over a general region.

Group A: I can find good approximations to functions, values of integrals and solutions to differential equations.

  • A1: I can approximate the value of an integral using the Trapezoidal Rule, Midpoint Rule, or Simpson's Rule.
  • A2: I can approximate the value of a solution to a differential equation using Euler's Method.
  • A3 (CORE): I can approximate a function with a Taylor polynomial.

Group S: I can determine whether series, including power series, converge.

  • S1 (CORE): I can show con(di)vergence of a series using the Direct Comparison Test.
  • S2: I can show con(di)vergence of a series using the Integral Test.
  • S3: I can find the interval and radius of convergence of a power series.
  • S4: I can prove a sequence converges using an $\epsilon$-$N$ argument.

Group E: I can bound the error associated with the above approximations.

  • E1 (CORE): I can bound the error when using the Trapezoidal Rule, Midpoint Rule, or Simpson's Rule.
  • E2 (CORE): I can bound the error of a Taylor polynomial using Taylor's Theorem.

Group O: I can find optimal solutions to multivariable functions.

  • O1: I can optimize a 3D function.