Professor Curious | Talk to an AI Tutor That Explains Until It Clicks

What is the formula for Average Rate of Change (AROC)?

$\frac{f(b) - f(a)}{b - a}$

Flip to see [answer/question]

Revise later

SpaceTo flip

If confident

All Flashcards

What is the formula for Average Rate of Change (AROC)?

$\frac{f(b) - f(a)}{b - a}$

What is the limit notation?

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

What does the Squeeze Theorem state?

If $g(x) \leq f(x) \leq h(x)$ for all x near a, and $\lim_{x \to a} g(x) = \lim_{x \to a} h(x) = L$ , then $\lim_{x \to a} f(x) = L$ .

What does the Intermediate Value Theorem (IVT) state?

If f is continuous on [a, b] and k is any number between f(a) and f(b), then there exists at least one number c in [a, b] such that f(c) = k.

What are the differences between removable and infinite discontinuities?

Removable: Limit exists, can be 'fixed'. Infinite: Vertical asymptote, limit DNE.

What are the differences between one-sided and two-sided limits?

One-sided: Limit from left or right. Two-sided: Limit from both sides, must be equal for the limit to exist.

What are the differences between average and instantaneous rate of change?

Average: Slope of secant line. Instantaneous: Slope of tangent line.