Evaluating Limits

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 if a limit is equal to DNE (Does Not Exist)?

Back

It means that the function does not approach any particular value as the input approaches a certain point.

Front

What is the limit of a constant function as x approaches any value?

Back

The limit is equal to the constant value of the function.

Front

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

Back

Substitute the value of x into the function, if the function is defined at that point.

Front

What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?

Back

The limit is 2, after factoring and simplifying the expression.

Front

What is the Squeeze Theorem in relation to limits?

Back

If f(x) ≤ g(x) ≤ h(x) for all x near a, and lim x→a f(x) = lim x→a h(x) = L, then lim x→a g(x) = L.

Front

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

Back

The limit is 1.

Front

What is the limit of (1/x) as x approaches infinity?

Back

The limit is 0.

Front

What is the limit of (x^3 - 3x^2 + 4) as x approaches 2?

Back

The limit is 2.

Front

What is the concept of one-sided limits?

Back

One-sided limits refer to the value that a function approaches as the input approaches a specific value from one side (left or right).