Math 130-03: Information for Test 2


The second test in this course is on Friday, March 23. It will cover Labs 4 through 7; Chapter 2, Sections 3 through 5; and Chapter 3, Sections 1 through 5. A significant part of what you need to know for the test is the list of differentiation formulas that we have encountered. Here is a list of formulas. In this list, $ c$ is a constant and $ f$ and $ g$ are functions.


\begin{displaymath} \begin{array}{l} \displaystyle \frac{d}{dx}\,c = 0 \\ \noal... ...\frac{d}{dx}\,\big(f(g(x))\big) = f'(g(x))g'(x)\\ \end{array}\end{displaymath}



Here are some other terms and ideas that you need to know:


epsilon-delta definition of limit
continuity at a point
continuity on an interval
continuity from the left or from the right
discontinuities
Intermediate Value Theorem
$ \displaystyle\lim_{x\to 0}\left(\frac{\sin(x)}{x}\right)=1$
limits involving trigonometric functions
secant lines and tangent lines
average velocity on an interval
instantaneous velocity on an interval
the derivative
formal definition of the derivative as a limit
relationship of derivative to slopes of tangent lines
relationship of derivative to instantaneous velocity
instantaneous rate of change
derivative as rate of change
various notations for derivative
second derivative, third derivative, etc.
differentiability at a point
differentiability on an interval
differentiability from the left or right
nondifferentiability
differentiability implies continuity
various rules for finding the derivative
marginal tax rate
zooming in on a function to find a derivative value
relating the graphs of $ f$ and of $ f'$