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

What does it mean for a function to be continuous at a point?

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 is the limit of a function as x approaches a?

Back

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

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 the limit of f(x) = 2x as x approaches 1?

Back

The limit is 2.

Front

What is the limit of f(x) = 1/x as x approaches 0?

Back

The limit does not exist (DNE) because the function approaches infinity.

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(x) and h(x) approach L as x approaches a, then f(x) also approaches L.

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

Back

One-sided limits consider the approach from one direction (left or right), while two-sided limits consider the approach from both directions.

Front

What is the limit of f(x) = x^2 as x approaches 3?

Back

The limit is 9.