A+ » VCE » Maths Methods U3 & 4 Master Notes » A3 Calculus » Continuity and Differentiability

# Continuity and Differentiability

## 1.5 Continuity and Differentiability (Not Required)

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

#### Continuity at a Point

• We only require an intuitive understanding of continuity. A function with rule f(x) is said to be continuous at x=a if the graph of y=f(x) can be drawn through the point with coordinates (a, f(a)) without a break. Otherwise, there is said to be a discontinuity at x=a.
• Mathematically and formally, continuity of a point is assured by the following:

i) f(x) is defined at x=a

ii) \lim _{x \rightarrow a} f(x)=f(a)

Example

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