Waste less time on Facebook — follow Brilliant.
×

Limits of Functions

What happens when a function's output isn't calculable directly – e.g., at infinity – but we still need to understand its behavior? That's where limits come in. See more

Misconceptions

Evaluate \[\lim_{x\to 5} 1.\]

True or False?

\[\lim_{x\to 0} \frac{1}{x} = \infty.\]

Suppose \(f(x)\) is a function defined on the real numbers and \[\lim_{x\to a} f(x) = L.\] Which of the following must be true?

Suppose \[\lim_{x\to \infty} f(x) = \infty \text{ and } \lim_{x\to \infty} g(x) = \infty,\]

and

\[L = \lim_{x\to \infty} (f(x) - g(x)).\]

Is it possible that \(L = 0\)?

Suppose \[\lim_{x\to \infty} f(x) = \infty \text{ and } \lim_{x\to \infty} g(x) = \infty,\]

and

\[L = \lim_{x\to \infty} (f(x) - g(x)).\]

Is it possible that \(L = -\infty\)?

×

Problem Loading...

Note Loading...

Set Loading...