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# Limit Notation

## 1.4 Algebra of Limits (Not Required)

• Any materials in this notes is not required in the scope of the course, but is included for your understanding.

#### Algebra of Limits

• Below are some properties of limits, assuming both \lim _{x \rightarrow a}f(x) and \lim _{x \rightarrow a}g(x) exists:

i) Sum:

\lim _{x \rightarrow a}[f(x)+g(x)]=\lim _{x \rightarrow a} f(x)+\lim _{x \rightarrow a}g(x)

ii) Difference:

\lim _{x \rightarrow a}[f(x)-g(x)]=\lim _{x \rightarrow a} f(x)-\lim _{x \rightarrow a} g(x)

iii) Multiple:

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## 1.1 Derivatives Basic Concepts – Rate of Changes

#### Average Rate of Change

• The average change of y with respect to x over the interval [a, b] is the gradient of the line connecting the points A(a,f(a)) and B(b,f(b)).

Note: [a,b] represents a range between a and b, inclusive. In other words, if x \in[a, b] , then \mid a \leq x \leq b . Also, we will always have a<b .

• It is given by:
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