Exam reviews
Exam reviews
(Coverage of topics has moved a bit over the years)
(Coverage of topics has moved a bit over the years)
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
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
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