Calculus
Limits of Functions
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 \(L = -\infty\)?