A List of Topics for Midterm 2
Disclaimer: This is not an official list. (Officially the midterm covers
sections 3.4-3.11 and 4.1-4.5.)
- Finding the tangent line to a given point
- Setting up equation to find horizontal tangent line of explicit
functions
- Derivatives of trigonometric functions (3.4)
- Computing limits using the fact lim(sin x)/x = 1 as x goes to 0 (3.4)
(L'Hospital usually works here too)
- Recognizing function compositions and using the Chain Rule (3.5)
- Implicit differentation for implicit functions (3.6)
- Setting up equations to find horizontal tangents of implicit
functions (3.6)
- Derivatives of inverse trigonometric functions (3.6)
- Computing higher derivatives (3.7)
- Derivatives of ln and log (3.8)
- Knowing when and how to use logarithmic differentiation (3.8)
- Derivatives of hyperbolic and inverse hyperbolic functions (3.9)
- Related rates: setting up variables and equations, then implicit
differentiation (3.10)
- Using linear approximation by choosing appropriate f, x, a (3.11)
- Differentials; computing maximum possible error, relative error, %
error (3.11)
- Knowing when and how to apply the closed interval method (4.1)
- Statement of Rolle's Theorem, Mean Value Theorem; finding c
satisfying their conclusions (4.2)
- Proving an identity using Corollary 4.2.7 (4.2)
- Finding critical points (4.1) and local max/min using sign of f '(x)
(4.3)
- f ''(x), concavity, inflection points (4.3)
- Second derivative test (4.3)
- When and how to use L'Hospital Rule for the limit of a quotient (4.4)
- Rewriting indeterminate products, differences, powers, then using
L'Hospital (4.4)
- Curve sketching checklist (the above and absolute max/min,
horizontal, vertical, slant asymptotes) (4.5)
Other study tips
- Review homework problems and make sure you know how to do them
- Check the solution manual at office hours
- Ask questions in section on Tuesday or at office hours
- Practice taking
the other version of quizzes you did not take
- The quizzes given in section were 1B, 2B, 3A, 4A, 5A, 6A, 7A
- Take the
practice midterm (to be up soon)
- Try the worksheet on 4.1-4.3 given in section October 21 (mainly try
1 and 2)