Module 1 (Limits)

What is another name for Calculus 1, and what does it study?

Differential Calculus.

The study of derivatives and their applications.

What is Rate of Change?

how fast a graph on one axis changes in relation to the other axis.

What is a Secant Line?

A line that goes through two points on a graph that does not have a constant slope. Used to calculate the approximate rate of change.

What is a Tangent Line?

A straight line through a single point on a function’s graph, whose slope is the derivative of that function at that point.

What is the formula for a Secant Line?

m(sec) = (f(x) - f(a))/(x - a)

What is the formula for Average Velocity?

v(ave) = (s(t) - s(a))/(t - a)

How do you find the approximate area of a curved graph?

Divide the area into rectangles, then add them up.

What is a Limit of a function?

The value a function approaches as you elevate it from one direction.

What is a Table of Functional Values?

A table that represents the values that the x-values of the function approach.

What is a One-Sided Limit?

The value the function approaches as the x-values approach the limit from one side only.

What is the Basic Limit Law?

For any real number (a) and any constant (c):

lim(x → a)x = a.

lim(x → a)c = c.

What are the 7 common Property Laws of Limits, besides the Basic Limit Law?

Sum Law.

Difference Law.

Constant Multiple Law.

Product Law.

Quotient Law.

Power Law.

Root Law.