Exam reviews
(Coverage of topics has moved a bit over the years)
Major topics include:
Average rate of change; instantaneous rate of change
Limits; limit rules; one-sided limits; limits involving infinity
Continuity; types of discontinuities (e.g. removable, jump, ...)
Limit definition of derivative
Derivative at a point; derivative as a function
Higher order derivatives; notation
Find tangent lines to curves
Sum, product, quotient rules for differentiation
Derivatives of x^k, e^x, sin(x), cos(x), tan(x), sec(x)
Differentiation and motion (velocity and acceleration)
Chain rule
Major topics include:
Implicit differentiation; derivative of inverse function
Derivatives of ln(x), arctan(x), arcsin(x), arcsec(x)
Logarithmic differentiation
Linearization and approximating function
Related rates problems
Absolute and local maximums and minimums
Identify critical points; classify critical points by use of either the first or second derivative tests
Setting up and solving optimization problems
Identifying when functions are increasing/decreasing; identifying when functions are concave up/down
Sketching functions
L'Hospital's rule for working with indeterminant limits
Newton's method for finding roots
Major topics include:
L'Hospital's rule for working with indeterminant limits
Newton's method for finding roots
Mean Value Theorem
Finding antiderivatives of basic functions x^k, e^x, sin(x), cos(x), sec^2(x), sec(x)tan(x), 1/(1+x^2), sec(x), and tan(x). Know that antiderivatives are unique up to "+C"
Use Riemann sums to approximate totals; definite integrals
Using basic properties of definite integrals (constant multiple, sums, inequalities, breaking into multiple parts, reversing order)
Compute average of a function over an interval
State and use both variations of the Fundamental Theorem of Calculus
Use substitution for definite and indefinite integration
Find the net area under a curve or between two curves
Integration and motion
Solve separable differential equations
Hyperbolic functions