Q. 5
Question
what we mean when we say that a limit exists, or that a limit does not exist.
Step-by-Step Solution
Verified Answer
If a limit exists then either x comes from a positive direction or a negative direction, function value approaches the same value.
If a limit does not exist then either the graph of the function has vertical asymptotes or the function has a gap at any value of x.
1Step 1. Condition of a limit exists.
If a limit exists then either x comes from a positive direction or a negative direction, function value approaches the same value.
2Step 2. Condition for a limit does not exist.
If the graph of the function is discontinuous or has any hole or gap at x value c then the limit does not exist.
If the graph of the function has a vertical asymptote at x value c then the limit does not exist.
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