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Mathematics Clinic => Calculus => Topic started by: bobbie on Jun 16, 2021

Title: What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x ...
Post by: bobbie on Jun 16, 2021

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.

Title: What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x ...
Post by: morrie123456 on Jun 16, 2021

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

Title: Re: What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x
Post by: J Tri on Sep 6, 2022

Thank you