Question

The function fff is defined over the real numbers. This table gives a few values of f.
x f(x)
2.9 9.62
2.99 9.85
2.999 9.99
3.001 9.99
3.01 9.85
3.1 9.62

What is a reasonable estimate for \displaystyle \lim_{x\to 3}f(x)
x→3
lim
​ f(x)?
Choose 1 answer:

(Choice A)
A
2.9

(Choice B)
B
3

(Choice C)
C
9.9

(Choice D)
D
10

(Choice E)
E
the limit does not exist

Answer 1

hello dear friend,
ur table is very complicated 
by the way as per my understanding, the limit f(x) is here representing the limits of "f"  as x approaches to 3

so now see ur table and the first three rows, f(x)' s values are approaching a distinct value as the values approaches to 3.

 as x is now increasing to x=3,(i.e, 2.99, 2.999...),
 so f (x) values is going towards 10.
 
 and in last three rows, x is now decreasing to x=3, f(x) values are approaching to 10.
 so a reasonable estimation for lim(x towards 3) f (x) is: 10
 
 so our required answer is 10 and D is correct answer.

Answer 2

u know friend ur table seems very confusing