CR Calculus Unit 1 Review: Limits and Continuity

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

Define continuity in the context of functions.

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

Front

What does it mean for a function to be discontinuous?

Back

A function is discontinuous at a point if it is not continuous at that point, meaning the limit does not equal the function's value.

Front

What is the formal definition of a limit?

Back

The formal definition of a limit states that for every ε > 0, there exists a δ > 0 such that if |x - c| < δ, then |f(x) - L| < ε.

Front

What is the difference between one-sided limits and two-sided limits?

Back

A one-sided limit considers the value of the function as it approaches from one side (left or right), while a two-sided limit considers both sides.

Front

What is the limit of a function as x approaches infinity?

Back

The limit of a function as x approaches infinity describes the behavior of the function as the input grows without bound.

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 it appropriately.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if f(x) is squeezed between g(x) and h(x) and both g and h have the same limit at a point, then f must also have that limit.

Front

How do you evaluate limits algebraically?

Back

To evaluate limits algebraically, you can substitute the value into the function, factor, rationalize, or use L'Hôpital's Rule if applicable.

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule is a method for finding limits of indeterminate forms by taking the derivative of the numerator and denominator.