April 21 - AP Calculus - Review #1

Front

What is the definition of continuity at a point?

Back

A function f is continuous at a point x = c if the following three conditions are met: 1) f(c) is defined, 2) the limit of f(x) as x approaches c exists, and 3) the limit equals f(c).

Front

What does it mean for a function to be continuous on an interval?

Back

A function is continuous on an interval if it is continuous at every point in that interval.

Front

How do you determine if a function is continuous at a specific point?

Back

To determine if a function is continuous at a point, check if the limit from the left equals the limit from the right and if both equal the function's value at that point.

Front

What is the limit of a function?

Back

The limit of a function as x approaches a value is the value that the function approaches as x gets arbitrarily close to that value.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining or redefining the function at that point.

Front

What is a non-removable discontinuity?

Back

A non-removable discontinuity occurs when a function cannot be made continuous at a point, often due to a vertical asymptote or a jump.

Front

What is the difference between left-hand limit and right-hand limit?

Back

The left-hand limit is the value that a function approaches as x approaches a point from the left, while the right-hand limit is the value that the function approaches as x approaches from the right.

Front

What is the Intermediate Value Theorem?

Back

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], then it takes on every value between f(a) and f(b) at least once.

Front

How do you find the limit of a rational function?

Back

To find the limit of a rational function as x approaches a value, substitute the value into the function. If it results in an indeterminate form, factor and simplify.