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U0S1V01 Introduction to Limits.txt
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U0S1V01 Introduction to Limits.txt
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#
# File: content-mit-18-01-1x-captions/U0S1V01 Introduction to Limits.txt
#
# Captions for MITx 18.01.1x module [nh5O6-2Evk8]
#
# This file has 32 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
Calculus has two main concepts-- the derivative
and the integral.
But in order to understand either of them,
you first have to understand limits.
So let's talk limits.
We'll start with a curve.
Fix a point A on the curve.
Choose a second point, B, which we're going to move.
And draw a line through A and B. Let's look
at what happens when B moves closer and closer to the point
A.
This is an example of a limit.
In the limit, the line becomes tangent to the curve
at the point A. The slope of this line
is the derivative at the point A. Now let's see how limits
are related to integrals.
Integrals are used to measure areas of curvy regions
like this.
Measuring areas of curvy regions seems hard,
but measuring areas of rectangles
is easy, so we'll try to fill our region with rectangles.
Each rectangle has a certain width.
As we make the width smaller, the total area
of the rectangles gets closer and closer
to the area of the curvy region.
The integral is the limit of the total area of the rectangles
as the width tends to zero.
So that's why we start with limits.
They're the foundation for everything else in calculus.
At the beginning, limits may seem abstract,
but very quickly you'll get used to them.