# 微积分网课代修|微分学代写Differential calculus代考|MTH295 Compositions

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## 微积分网课代修|微分学代写Differential calculus代考|Compositions

Definit ion 1.8.1: composition of functions
Suppose we have two functions (with the codomain of the former matching the domain of the latter):
$F: X \rightarrow Y$ and $G: Y \rightarrow Z$
1.8. Compositions
80
Then their composition is the function (from the domain of the former to the codomain of the latter)
$$H: X \rightarrow Z,$$
which is computed for every $x$ in $X$ according to the following two-step procedure:
$$x \rightarrow F(x)=y \rightarrow G(y)=z .$$z

## 微积分网课代修|微分学代写Differential calculus代考|Numbers are limits

So, limits (when finite) are numbers, and vice versa.
However, as we just saw, a number can be the limit of many sequences:
$\begin{array}{ccccccc}.9 & .99 & .999 & .9999 & .99999 & \ldots & \rightarrow 1 \ 1 . & 1.1 & 1.01 & 1.001 & 1.0001 & \ldots & \rightarrow 1\end{array}$
Infinitely many, in fact:
We, therefore, act in reverse:
Instead of looking for the limit of a sequence, we find sequences that converge to a number we are interested in.
We think of those as approximations of this number.

## 微积分网课代修|微分学代写Differential calculus代考|Compositions

$F: X \rightarrow Y$ 和 $G: Y \rightarrow Z$
1.8. Compositions
80

$$H: X \rightarrow Z,$$

$$x \rightarrow F(x)=y \rightarrow G(y)=z .$$

## 微积分网课代修|微分学代写Differential calculus代考|Numbers are limits

$\begin{array}{llllllllllllll}.9 & .99 & .999 & .9999 & .99999 & \ldots & \rightarrow 1 & 1 . & 1.1 & 1.01 & 1.001 & 1.0001 & \ldots & \rightarrow 1\end{array}$