All Flashcards

What is the notation for a limit?

$\lim_{x \to a} f(x) = L$

What is the notation for a right-hand limit?

$\lim_{x \to a^+} f(x) = L$

What is the notation for a left-hand limit?

$\lim_{x \to a^-} f(x) = L$

What form indicates that direct substitution won't work?

$\frac{0}{0}$

What does the Existence of a Limit Theorem state?

$\lim_{x \to a} f(x)$ exists if and only if $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$ .

What are the differences between using direct substitution and tables to find limits?

Direct Substitution: Simple, but fails for indeterminate forms. | Tables: Useful for indeterminate forms, but requires more computation and careful observation.

What are the differences between left-hand and right-hand limits?

Left-hand Limit: Approaching from values less than 'a'. | Right-hand Limit: Approaching from values greater than 'a'.