Limits 2

Front

What is the definition of 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 limit to exist?

Back

A limit exists if the function approaches the same value from both the left and right sides as the input approaches a certain point.

Front

What is the formal definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

Front

What is the relationship between limits and continuity?

Back

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

Front

What is the limit of a constant function?

Back

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

Front

How do you evaluate the limit of a polynomial function as x approaches a value?

Back

Substitute the value of x into the polynomial function.

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule states that if the limit results in an indeterminate form (0/0 or ∞/∞), you can take the derivative of the numerator and denominator and then evaluate the limit.

Front

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

Back

The limit of sin(x)/x as x approaches 0 is 1.

Front

What is a one-sided limit?

Back

A one-sided limit is the value that a function approaches as the input approaches a certain point from one side only (left or right).

Front

What is the squeeze theorem?

Back

The squeeze theorem states that if a function is squeezed between two other functions that have the same limit at a point, then the squeezed function also has that limit.