One-sided Limits on a Graph

[nycmathguy]

Calculus
Section 1.5

The limit of f(t) as t tends to 12 from the left and right is 150. What is the significance of these one-sided limits? IDK.

You say?

 

[MathLover1]

One-sided limits are denoted by placing a positive (+) or negative (-) sign as an exponent
on the value “a”. For example, if you wanted to find a one-sided limit from the left then the limit
would look like

. This limit would be read as “the limit of f(x) as x approaches a from the left.”
A right-handed limit would look like

and would be read as “the limit of f(x) as
x approaches a from the right.”

Finding one-sided limits are important since they will be used in determining if the two- sided limit exists. For the two-sided limit to exist both one-sided limits must exist and be equal to the same value.

 

[nycmathguy]

View attachment 2445

One-sided limits are denoted by placing a positive (+) or negative (-) sign as an exponent
on the value “a”. For example, if you wanted to find a one-sided limit from the left then the limit
would look like View attachment 2443 . This limit would be read as “the limit of f(x) as x approaches a from the left.”
A right-handed limit would look like View attachment 2444 and would be read as “the limit of f(x) as
x approaches a from the right.”

Finding one-sided limits are important since they will be used in determining if the two- sided limit exists. For the two-sided limit to exist both one-sided limits must exist and be equal to the same value.

Thank you for the study notes. Now, is my answer for the limit correct?