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# Difference

## 10.1 Algebraic Properties of Antiderivatives

#### Algebraic Properties of Indefinite Integrals

• There are a few algebraic properties for antiderivatives:

i) Sum

\int f(x)+g(x) d x=\int f(x) d x+\int g(x) d x

ii) Difference

\int f(x)-g(x) d x=\int f(x) d x-\int g(x) d x

iii) Scalar Multiple

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## 4.1 Sums and Differences

#### Linear Operation Rules

• There are several rules in differentiation. Let’s start with these:

i) If f(x)=c where c is a constant, then f^{\prime}(x)=0 (Constant function)

ii) If f(x)=k \cdot g(x), then f^{\prime}(x)=k \cdot g^{\prime}(x) (Multiple)

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## 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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