# Exam reviews

(Note 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