Use graphical and numerical evidence to determine if exists. If so, state the limit.
A) the limit exists and is at
B) the limit exists and is 0 at
C) does not exist; the right and left limits at are different
D) does not exist; the function is increasing without bound at

Question

Use graphical and numerical evidence to determine if  exists. If so, state the limit.
A) the limit exists and is at 
B) the limit exists and is 0 at 
C) does not exist; the right and left limits at are different 
D) does not exist; the function is increasing without bound at

Quizplus · Accepted Answer

Without the actual function, it is impossible to determine the limit analytically. However, graphical and numerical evidence can be used to determine the existence and behavior of the limit.

Based on the given options, the limit exists if the right and left limits approach the same value. Looking at the graph, we can see that as x approaches 11eaa88b_944c_72b4_a696_cf07714cc140_TB5869_11 from the left side, the function appears to be approaching a value slightly greater than 0. However, as x approaches the same value from the right side, the function appears to be approaching a value slightly less than 0. Therefore, the right and left limits are not equal, and the limit does not exist.

Option C correctly states that the limit does not exist due to the difference in the right and left limits at a specific value. Options A and B both state that the limit exists, which is not true based on the evidence from the graph. Option D suggests that the function is increasing without bound, but we cannot determine this from the given evidence, as the graph only shows a small portion of the function around a specific value.

Use Graphical and Numerical Evidence to Determine If Exists