Pre calculusLimits Flashcard 1

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 if a limit is DNE (Does Not Exist)?

Back

It means that the function does not approach a specific value 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

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

Back

You can evaluate the function at that value, or use algebraic manipulation, or apply limit laws.

Front

What is the limit of a function as x approaches infinity?

Back

It describes the behavior of the function as the input grows without bound.

Front

What does it mean for a limit to approach infinity?

Back

It means that the function's values increase without bound as the input approaches a certain value.

Front

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

Back

The limit is positive infinity.

Front

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

Back

The limit is negative infinity.

Front

What is the Squeeze Theorem?

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 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.