# Calculus I Review: Curve Sketching

Curve sketching is an important application of derivatives. Here’s an example with a polynomial, with pictures to help assist understanding:

# Precalculus Resources: Spring 2017 Midterm II Review

I have gathered quizzes that relate directly to the upcoming midterm, as well as included a sample midterm. Please feel free to use these for practice! If you have trouble with the material, visit this page for additional resources. Don’t forget to grab a free version of wolfram alpha pro to help you if you’re enrolled at San Francisco State University!

## Topics Covered:

• 2.4: Polynomials
• Vertex of a parabola
• Determine the behavior of a polynomial near $- \infty$ or $\infty$
• 2.5: Rational Functions
• Determine the behavior of rational functions near $- \infty$ to $\infty$
• Determine the vertical and horizontal asymptotes of a rational function
• Determine the holes of a rational function, if they exist.
• 3.1: Exponential and Logarithmic Functions
• Their definitions as inverses
• Practice using #23 – #32 in Precalculus – Prelude to Calculus, 3rd Ed.
• 3.2: Power Rule
• Change of Base
• 3.3: Product and Quotient Rule
• Read p.249-p.252 for applications in scientific settings
• 3.4: Exponential Growth
• Compound Interest (n times per year)
• 3.5: e and the Natural Logarithm
• Understanding the definition of e will enhance your understanding of proofs later on. For now, we know it’s a real number that is approximately equal to 2.71, and it’s associated with Continuous growth!
• 3.7: Exponential Growth Revisited
• Read p.304-p.306 for an application of the approximation methods discussed in 3.6 used in financial estimations.
• Focus on Continuous Compound Interest
• 4.1: Unit Circle