Behavior of a function near a particular input.

The limit of a function ƒ(x) is L

as L approaches a

lim_{x → a}ƒ(x) = L

The right limit of a function ƒ(x) is A

as x approaches a from the right

lim_{x → a+}ƒ(x) = A

The left limit of a function ƒ(x) is A

as x approaches a from the left

lim_{x → a-}ƒ(x) = A

lim_{x → 3}2x = 6 since 2(3) = 6

Given a constant c,

If ƒ(x) = c then

lim_{x → a}ƒ(x) = c

Given a constant k:

lim_{x → a}ƒ(x)kA = k * lim_{x → a}ƒ(x)

Use the limit theorem with a multiplier:

lim

lim

lim

lim

lim_{x → a}[ƒ(x) + g(x)] =

lim_{x → a}ƒ(x) + lim_{x → a}g(x)

lim

[2(3) + 3

[6 + 9] = 6 + 9

15 = 15

ƒ(x) = 2x and g(x) = xlim_{x → a}[ƒ(x) - g(x)] =

lim_{x → a}ƒ(x) - lim_{x → a}g(x)

lim

[2(3) - 3

[6 - 9] = 6 - 9

-3 = -3

ƒ(x) = 2x and g(x) = xlim_{x → a}[ƒ(x) * g(x)] =

lim_{x → a}ƒ(x) * lim_{x → a}g(x)

lim

[2(3) * 3

[6 * 9] = 6 * 9

54 = 54

lim_{x → a}[ƒ(x) / g(x)] =

lim_{x → a}ƒ(x) / lim_{x → a}g(x)

This lesson walks you through what limit is, how to write limit notation, and limit theorems

- constant
- a value that always assumes the same value independent of how its parameters are varied
- difference
- the result of one of the important mathematical operations, which is obtained by subtracting two numbers
- function
- relation between a set of inputs and permissible outputs

ƒ(x) - input
- what goes into a function
- limit
- the value that a function (or sequence) approaches as the input (or index) approaches some valu
- limit of a function
- product
- The answer when two or more values are multiplied together
- theorem
- A statement provable using logic
- variable
- Alphabetic character representing a number

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