April 2023
Beginner to intermediate
656 pages
17h 28m
English
Content preview from Calculus All-in-One For Dummies (+ Chapter Quizzes Online)
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Chapter 3
Why Calculus Works
IN THIS CHAPTER
Using limits to zoom in on curves
Slope equals rise over run
Area of a triangle equals one-half base times height
The Pythagorean Theorem: 
In Chapters 1 and 2, I talk a lot about the process of zooming in on a curve till it looks straight. The mathematics of calculus works because of this basic nature of curves — that they’re locally straight — in other words, curves are straight at the microscopic level. The earth is round, but to us it looks flat because we’re sort of at the microscopic level when compared to the size of the earth. Calculus works because after you zoom in and curves look straight, you can use regular algebra and geometry with them. The zooming-in process is achieved through the mathematics of limits.
The Limit Concept: A Mathematical Microscope
The mathematics of limits is the microscope that zooms in on a curve. Here’s how a limit works. Say you want the exact slope or steepness of the parabola at the point . See ...
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.