Consider the table of data for the function g(x),below:
x: 2.9, 2.99, 2.999, 3.01, 3.1
g(x):4.41, 4.9401, 4.994, -5.006, -5.0601, -5.61
From the data given, it would apPear the lim g(X) x--> 3 is likely to be:
A. 3
B. -5
C. Does not exist
D. 5
E. -5.61
I thinks it C or D not sure because it doesn't say what direction it's approaching from.
To determine the limit of g(x) as x approaches 3, we need to analyze the behavior of the function on both sides of x = 3. Based on the given data, we can observe that as x approaches 3 from the left (values less than 3), g(x) tends to -5.006. On the other hand, as x approaches 3 from the right (values greater than 3), g(x) tends to -5.0601.
Since the function has different values as x approaches 3 from the left and right, we can conclude that the limit of g(x) as x approaches 3 does not exist. Hence, the correct answer is option C: Does not exist.