Important Dates and Reminders

Hello Professor Baker's Math Class!

  • No Class: Thursday, December 8th. Use this time wisely to work on your take-home test.
  • Take Home Test Due: December 15th (the day of the final exam)
  • Final Exam Review: We will conduct an in-class review session on December 13th to help you prepare.
  • Final Exam: December 15th

Chapter 5 Take Home Test

Remember to show all your work and clearly indicate your answers. Here are a few key concepts you'll want to be familiar with for the test. The test contains integration problems, including:

  • Indefinite and definite integrals
  • Trigonometric integrals (integrals involving $\sin x$, $\cos x$, $\sec^2 x$, etc.)
  • Integrals involving algebraic functions (polynomials, radicals)

Here are some example problems, similar to what you might find on the test:

  1. Evaluate the definite integral: $\int_{0}^{1} (1 - x^9) dx$
  2. Evaluate the definite integral: $\int_{1}^{9} \frac{\sqrt{x} - 2x^2}{x} dx$
  3. Evaluate the definite integral: $\int_{0}^{2\pi} \sin x - \cos x dx$
  4. Find the indefinite integral: $\int \sec^2 x dx$
  5. Find the indefinite integral: $\int \frac{1}{x^2+1} - \frac{1}{\sqrt{1-x^2}} dx$

The test also covers applications of integration, such as:

  • Finding displacement and distance traveled given a velocity function.

For example:

  • Given the velocity function $v(t) = t^2 - 2t - 3$, find the displacement of the particle between $t=2$ and $t=4$. Remember that displacement is found by calculating the definite integral $\int_{2}^{4} v(t) dt$.
  • Given the velocity function $v(t) = t^2 - 2t - 3$, find the *distance* the particle traveled between $t=2$ and $t=4$. Remember you will need to consider when the velocity is negative and positive by taking the absolute value of the integral $\int_{2}^{4} |v(t)| dt$.

Final Exam Review

The final exam will cover a broad range of topics from the course. The in-class review on December 13th will be very helpful, so please attend! Key topics to review include:

  • Differentiation rules (power rule, product rule, quotient rule, chain rule)
  • Applications of derivatives (finding tangent lines, local extrema, inflection points, optimization problems)
  • Limits (including L'Hôpital's Rule)
  • Integration techniques

Here are some sample problems from the review sheet:

  1. Find the second derivative, $y''$, of $y = (x^2 + x^3)^2$.
  2. Find the first derivative, $y'$, of $y = \frac{x^2 - x + 2}{\sqrt{x}}$.
  3. Find the second derivative, $y''$, of $y = x^2 \sin(\pi x)$.
  4. Find $lim_{x \to 0} \frac{e^{2x} - e^{-2x}}{ln(x+1)}$ using L'Hopital's Rule.

Good luck with your studying and test preparation! Please reach out to Professor Baker during office hours or post questions on the discussion forum if you need help.