We already know from the definition of continuity at a point that the graph of a function will not have a hole at any point where it using the intermediate value theorem.
48+ Intermediate Value Theorem Calculus PNG. The idea behind the intermediate value theorem is this: To work this problem, he uses the definition of the limit.
(PDF) First Semester Calculus Students' Understanding of ... from i1.rgstatic.net
This example shows how the intermediate value theorem only ensures output values between f(a) and f(b) even though there are more values outside this part of the range. Your teacher probably told you that you can draw the graph of a continuous function without lifting your pencil off the paper. I \to \r$ be continuous on $i$.
What mathematics do i need to know before i can understand a rigorous proof for the fundamental theorem of calculus?
Basically, it's the property of continuous functions that guarantees no gaps in the graph between two given points. Here we see a consequence of a function being continuous. The intermediate value theorem should not be brushed off lightly. Intermediate value theorem explained in plain english with example of how to apply the theorem to a line segment.
