SUNY Geneseo Department of Mathematics
Math 221 02
Fall 2020
Prof. Doug Baldwin
This discussion reinforces ideas from “Continuity over an Interval” and “The Intermediate Value Theorem” in section 2.4 of the textbook, and begins looking at some of the theoretical results in those sections.
Please post at least one response to at least one of the following by class time Friday:
Here is the same hypothetical function as you saw in the first continuity discussion:
Assume that each tick mark on the horizontal axis is 1 unit. Is this function continuous over the interval [0,1]? How about the interval (0,1)? (1,3]? (1,3)?
Do you have any questions about the interval notations (a,b), [a,b], (a,b], etc?
Assume (as is the case) that sine and cosine are continuous functions. What are
\[\lim_{x \to \pi} \cos \frac{x}{2}\] \[\lim_{a \to 1} \sin \left(\frac{\pi(a^2 - a)}{a-1}\right)\]Most outer space science fiction movies involve spaceships that fly faster than the speed of light.
According to Einstein’s theory of special relativity, it takes infinite energy for an object with any mass at all to move at the speed of light.
Assume that science fiction spaceships have mass, and that even in science fiction movies it’s impossible to have an infinite amount of energy.
When a science fiction spaceship accelerates from below the speed of light to above, can its speed be a continuous function of time, or must it be discontinuous? Why?