Question

The function f(x) has values as given in the table below.

x 4.9 4.99 4.999 5.001 5.01 5.1
f(x) 10 100 1000 –1000 –100 –10


Find
lim
x→5
f(x), if it exists.

–1000
0
1000
DNE

Answer 1

The limit of the function f(x) as x approaches 5 does not exist.

Therefore, the correct answer is: option 'DNE'.

Step-by-step explanation:

To find the limit of the function f(x) as x approaches 5, we need to examine the behavior of the function as x gets closer and closer to 5.

Looking at the table of values for f(x), we can see that as x approaches 5 from the left side (x < 5), the values of f(x) become increasingly negative, approaching -1000.

As x approaches 5 from the right side (x > 5), the values of f(x) become increasingly positive, approaching 1000.

Since the left-hand and right-hand limits are different, the overall limit does not exist.

Therefore, the answer is DNE (does not exist).