Limits Review

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 limit of a constant function?

Back

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

Front

What is the limit as x approaches infinity for the function f(x) = 1/x?

Back

The limit is 0.

Front

What does DNE stand for in the context of limits?

Back

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

Front

How do you find the limit of a function at a point where it is not defined?

Back

You can use techniques such as factoring, rationalizing, or applying L'Hôpital's rule.

Front

What is the limit as x approaches 4 for the function f(x) = (x^2 - 16)/(x - 4)?

Back

The limit is 8.

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 as x approaches 7 from the right for the function f(x) = 1/(x-7)?

Back

The limit is +∞.

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 c, then f(x) also approaches L.