More Basic Limits that you may encounter

This is a follow-up for previous posts with an example

In iv) a is not in the domain of the function. Limit as x approaches a does not exist because left hand side limit is not equal to right hand side limit.
In v) a is in the domain although there is a vertical asymptote shown in the graph. Limit as x approaches a from left side of f(x) is equal to L1(some number) and limit as x aprroaches a from right of f(x) is equal to infinity. Hence, limit as x approaches a does not exist. However, the limit as x approaches a from left side exist.

In 6) a is not in the domain because there is a vertical asymptote in the graph. However, more accurate answer to why a is not in the domain is: because limit from left hand side goes to (+)infinity and limit as x approaches a from right hand side goes to negative infinity.
In 7) a is not in the domain. Limit as x approaches a from left side is (-) infinity and limit as x approaches a from right side is also (-) infinity. Hence, limit as x approaches a is (-) infinity.

in Example (E): f(x) = ln x  

domain: (0, ∞) all numbers greater than 0

lim as x approaches 0 from right is (-) infinity

limit as x approaches 0 from right is not possible because it is out of the domain.

since limit as x approaches 0 from right of f(x) is (-) infinity, at x=0 there exists a vertical asymptote.