Calculus

Limit 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 $L = -\infty$?

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