Solve the problem.
-What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a?

A) The limit of f(x) as x-a from the left exists, the limit of f(x) as x-a from the right exists, and these two limits are the same.

B) f(a) exists, the limit of f(x) as x-a from the left exists, and the limit of f(x) as x-a from the right exists.

C) The limit of f(x) as x-a from the left exists, the limit of f(x) as x-a from the right exists, and at least one of these limits is the same as f(a).

D) Either the limit of f(x) as x-a from the left exists or the limit of f(x) as x-a from the right exists

Question

Solve the problem.
-What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a?

A) The limit of  f(x) as x-a  from the left exists, the limit of  f(x) as x-a  from the right exists, and these two limits are the same. 
 
B) f(a) exists, the limit of  f(x) as x-a   from the left exists, and the limit of   f(x) as x-a  from the right exists. 
 
C) The limit of  f(x) as x-a   from the left exists, the limit of   f(x) as x-a  from the right exists, and at least one of these limits is the same as f(a). 
 
D) Either the limit of   f(x) as x-a   from the left exists or the limit of   f(x) as x-a   from the right exists

Quizplus · Accepted Answer

For a function f(x) to have a limit as x approaches a, the left-hand limit and the right-hand limit must both exist and be equal.

Solve the Problem. -What Conditions, When Present, Are Sufficient to Conclude That a Conclude