Calculus Review - Limits & Continuity

Front

What is the limit?

Back

The limit of a function is the value that the function approaches as the input approaches a certain value.

Front

Evaluate lim_x→0 sin(6x) ∕ sin(2x)

Back

3

Front

What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that a limit cannot be determined.

Front

What is continuity in calculus?

Back

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

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 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.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a.

Front

How do you determine if a function has a vertical asymptote?

Back

A function has a vertical asymptote at x = a if the limit of the function approaches infinity or negative infinity as x approaches a.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if f(x) ≤ g(x) ≤ h(x) for all x near a, and the limits of f and h as x approaches a are equal, then the limit of g as x approaches a is also equal to that limit.

Front

What is the limit of a constant function?

Back

The limit of a constant function as x approaches any value is the constant itself.