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What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x ...

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bobbie:
What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a?
◦ Either the limit of  as  from the left exists or the limit of  as  from the right exists
◦ The limit of  as  from the left exists, the limit of  as  from the right exists, and at least one of these limits is the same as f(a).
◦ f(a) exists, the limit of  as  from the left exists, and the limit of  as  from the right exists.
◦ The limit of  as  from the left exists, the limit of  as  from the right exists, and these two limits are the same.

morrie123456:
The limit of  as  from the left exists, the limit of  as  from the right exists, and these two limits are the same.

J Tri:
Thank you

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