MAT112 Test 2 Topics
- limits
- from left, right
- types of problems (when limits don't exist)
- rules for limits
- limits at infinity (especially rational functions)
- continuity
- relates to connectedness (can draw the graph without lifting
the pencil from the paper)
- types of discontinuities:
- holes
- jumps
- vertical asymptotes
- types of functions continuous on their domains
- Intermediate Value Theorem
- Rate of change
- average rate of change
- instantaneous rate of change
- link to the slope of a line (secant or tangent)
- Derivative
- definition as a limit
- the instantaneous rate of change of the function
- slope of the tangent line
- relates to smoothness (no corners; must be continuous)
- types of functions differentiable on their domains
- Derivative rules:
- constant functions
- constant times a function
- "derivative of a sum is the sum of the derivatives"
- "derivative of a difference is the difference of the derivatives"
- power rule
- product rule
- quotient rule ("lo dee hi minus hi dee lo, over the denominator
squared they go!")
- Derivatives of exponential and logarithmic functions
- Chain rule:
- [f(stuff)]' = f'(stuff) stuff '
- [estuff]' = estuff stuff '
- [ln(stuff)]' = stuff '/stuff
Website maintained by Andy Long.
Comments appreciated.
Updated on 09/21/2012 18:24:52