Question

In a function, if limit do not exist at a domain value x= a, then function is _________.

Answer 1

Answer:

not defined

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Answer 2

Answer:

Undefined with T&C*

Step-by-step explanation:

* Not necessarily, The domain of a function tells you over what values the function f(x) exists, not where it is continuous. Take the piecewise function:

f(x)= {1 x<0

{2 x≥0

This function is defined for all x∈R, but is not continuous at x=0. It still has a valid value: f(0)=2, but that doesn't make it continuous at that point.

For a function to be continuous at a point, its limit must be the same regardless of what direction of approach. In this case, limx→0−f(x)=1 while limx→0+f(x)=2, making it discontinuous at that point.