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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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5.5 Sum and Product of Functions

Sum and Product of Functions

• Different functions can be added or multiplied together.
• Say there is two functions f(x) and g(x). We write their sum as (f+g)(x), and product as (fg)(x). In particular, f+g is the sum, fg is the product.
• Thus, to be clearer, it simply means

\begin{aligned} (f+g)(x) &=f(x)+g(x) \\(f g)(x) &=f(x) g(x)\end{aligned}

• When performing such functions, we have to be aware of the domain. For the sum and product to be defined, the domain of this combined function must be in both the domain of f and g.
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Exponential and Logarithm Functions

This tutorial covers material encountered in chapter 5 of the VCE Mathematical Methods Textbook, namely: Exponential functions Index laws Log functions Log laws and change… Read More »Exponential and Logarithm Functions

Basic Functions and Relations

This tutorial covers material encountered in chapter 1 of the VCE Mathematical Methods Textbook, namely: The domain and range of basic relations/functions The maximal domain… Read More »Basic Functions and Relations