HELIXPrep › Engineering Mathematics › Change
Section 1 · Module 1.1 · Topic 2
| Time | Cells |
|---|---|
| 1:00 PM | 1,000 |
| 2:00 PM | 1,200 |
| 3:00 PM | 1,400 |
| 4:00 PM | 1,600 |
| 5:00 PM | 1,800 |
| 6:00 PM | 2,000 |
| 7:00 PM | 2,200 |
But what was the growth rate at exactly 1:37 PM?
We can't measure at a single instant — but we can shrink the interval around it and see what happens.
Magnification
Field view — multiple bacteria visible
Does the bacterium change
when magnification increases?
Use the zoom slider to investigate what happens to y as x approaches 2.
Low zoom — parabola looks broad and curved
A Weird Case
At x = 1 this function is undefined. Can a limit still exist?
Move the slider to approach x = 1 from both sides
Formal Notation
What value does f(x) approach as x approaches a?
What does a limit describe?
Imagine measuring growth rate
over smaller and smaller time intervals.
Which mathematical idea allows us to talk about growth at a single instant?
A value tells you where you are.
A limit tells you where you are heading.
What's Coming Next
Next concept is what happens
When Limits Fail
(Continuity)
Create a free account to track your progress, earn XP, and unlock every free module on HELIXPrep.
Create Free Account →