Explanation
We have the following limit:
[tex]\lim_{n\to9}g(x)=5.[/tex]
To determine which table best reflects function g(x) values, we analyse the limit.
0. x → 9 means that we must analyze the function g(x) in the range of values of x very near the value x = 9.
,
1. lim = 5 means that for the values of x very near to x = 9, the value of the function must be a number near to 5.
1) From point 1, we can discard the second option because the table shows values of x near x = 5, not x = 9.
2) From point 2, we can discard the first and fourth options:
• the first option shows a jump up from the value y = 4.997 to y = 10.030,
,
• the fourth option shows a jump down from the value y = 100.00 to y = 4.570.
3) The third option is the correct one. It has values of y near to y = 5 for values of x near to x = 9.
Answer
Third option
