Slope-Intercept Form

y = mx + b

Slope (m)

Rise / Run

y_{2}-y_{1}/x_{2}-x_{1}

Point-Slope Form

y - y_{1} = m(x-x_{1})

What happens to the slope of the secant line as b approaches a?

It approaches the slope of the tangent line

m_{sec} --> m_{tan}

What is a secant line?

A straight line joining two points on a function.

What does the secant line represent?

The average rate of change of a function between two points.

Average Velocity =

Total Distance / Total Time

Change in distance over time

Instantaneous Velocity

Velocity at a specific time

Definition of a Limit

Suppose f(x) is defined when x is near the number a (This means that f is defined on some open interval that contains a, except possibly a itself.)

The limit of f(x), as x approaches a equals L if we can make the value of f(x) arbitrarily close to L by taking x to be sufficiently close to a (on either side of a) but not equal to a

Basic Limit Formula

What are the two ways to estimate a limit?

1. Evaluate f(x) at points near a.

2. Trace the graph and see y values

When are cases when a limit does not exist?

1. Oscillating functions

2. When the value of L is different on two sides

L is a unique value

Definition of a Left-Handed Limit

The left-handed limit of f(x) as x approaches a (or the limit of f(x) as x approxhes a from the left) is equal to L if we can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close to a and x less than a.

Definition of a Right-Sided Limit

The right-hand limit of f(x) as x approxhes a (or the limit of f(x) as x approaches a from the right) is equal to L if we can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close to a and x greater than a.

Limit Theorem