The function is a continuous function at 2 if the LHL and RHL will be the same as the limit of the function.
What is continuity of a function?
It is defined as the property of a function in which the function varies continuous, and we plot the graph of a function it doesn't break.
We have a function:
[tex]\rm f(x) = \left \{ {{x^2-x}, x\leq 2\atop {2x - 2 \ ,x > 2 \ } \right.[/tex]
If f(x) is a continuous, then it will follow:
f(2) = 2² - 2 = 4 - 2 = 2
Left-hand limit at 2 = right-hand limit at 2 = 2
Limit at 2 of a function = 2
Using limit, we can check the whether the function is differentiable or not.
Thus, the function is a continuous function at 2 if the LHL and RHL will be the same as the limit of the function.
Learn more about the continuous function here:
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