- #1
woundedtiger4 said:
fzero said:
The down and up arrows in a limit notation represent the direction from which the limit is being approached. The down arrow indicates the limit from the left, while the up arrow indicates the limit from the right.
To read a limit notation with down and up arrows, start with the variable being approached by the limit (e.g. x), followed by the down arrow for the limit from the left or the up arrow for the limit from the right. Then, write the value that the variable is approaching (e.g. 5) after the arrow (e.g. x → 5) to read "the limit of x as it approaches 5."
The down and up arrows in a limit notation provide more information about the direction in which the variable is approaching the limiting value. This helps to clarify the behavior of the function at that specific point.
Yes, the order of the down and up arrows matters in a limit notation. The down arrow always comes before the up arrow, indicating that the limit from the left is evaluated first, followed by the limit from the right.
To evaluate a limit with down and up arrows, you first evaluate the limit from the left by plugging in values slightly less than the limiting value for the variable. Then, evaluate the limit from the right by plugging in values slightly greater than the limiting value. If both limits exist and are equal, then the overall limit exists and is equal to the common value of the left and right limits.
