Limits

Front

What is a limit in calculus?

Back

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

Front

How do you denote the limit of a function f(x) as x approaches a value a?

Back

It is denoted as lim (x -> a) f(x).

Front

What does it mean for a limit to exist?

Back

A limit exists if the function approaches a specific value as the input approaches a certain point from both sides.

Front

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

Back

The limit is 6, since f(3) = 2(3) = 6.

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 both directions.

Front

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

Back

The limit is +∞.

Front

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

Back

The limit is -∞.

Front

What is a continuous function?

Back

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

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, then f also has that limit.

Front

What is the limit of sin(x)/x as x approaches 0?

Back

The limit is 1.