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Intuition for Theorems About Continuous Functions

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Explanations 2

Suppose you're drawing back and forth on a number line (a one-dimensional figure), without ever lifting your pencil. Let's say you start at time t=0t=0t=0 (your pencil first tou…
By Victor Wang, Toan Pham
Intuitively, a continuous function can be thought of a function that can be drawn without raising your pencil off the page. For instance What is most important to note is that
By Evan Fang

Problems 1

Say you're drawing on the number line for time in the interval [0,10][0, 10][0,10] such that at time ttt, your pencil is at position g(t)=t2−6t+10g(t) = t^2 - 6t + 10g(t)=t2−6t+…