Calculus 1 Common Topics List1
1. Functions
(a) polynomials, rationals, exponentials, logarithmic, trigonometric, arctan, absolute
value, radicals, power function
i. graphs
ii. continuity properties
(b) inverse functions
(c) composition of functions
(d) functional notation
(e) functions of two variables, i.e. f(x, y)
2. Limits
(a) intuitive definition
i. graph
ii. table
(b) right- and left-hand limits
(c) analytical procedures for computing limits
(d) limit laws (properties of limits)
(e) indeterminate forms (∞
∞and 0
0)
(f) successive approximations (judging accuracy subjectively through iterations, i.e.
two approximations of the same result are better than one)
3. Continuity
(a) intuitive/graphical understanding
(b) list of functions that are continuous on their domains
(c) recognizing discontinuities in a function given by a formula
(d) definition of continuity (“limit” definition)
1This list was approved at the 8/28/09 Math Departmental retreat
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