# Exam reviews

(Note coverage of topics has moved a bit over the years)

## Basics of differentiation

### 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

## Basics of integration

### 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