Continuity at a Number | Continuous Functions | Basic Calculus
Basic Calculus
Continuity at a Number
A function is continuous when its graph is a single unbroken curve. That you could draw without lifting your pen from the paper.
A function 𝑓(𝑥) is said to be continuous at the number 𝑎 if all of the following three conditions are satisfied.
𝒇(𝒂)𝒆𝒙𝒊𝒔𝒕𝒔
(𝒍𝒊𝒎)┬(𝒙→𝒂)𝒇(𝒙)𝒆𝒙𝒊𝒔𝒕𝒔
(𝒍𝒊𝒎)┬(𝒙→𝒂)〖𝒇(𝒙)=𝒇(𝒂)〗
If any one of the above three conditions fail, the function 𝑓(𝑥) is said to be discontinuous at a number 𝑎.
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