Question

I have a practice problem in the calculus subject, I’m having trouble solving it properly

Answer 1

The limit of a function is the value that a function approaches as that function's inputs get closer and closer to some number.

The question asks us to estimate from the table:

$\lim _{x\to-2}g(x)$

To find the limit of g(x) as x tends to -2, we need to check the trend of the function as we head towards -2 from both negative and positive infinity.

From negative infinity, the closest value we can get to before -2 is -2.001 according to the values given in the table. The value of g(x) from the table is:

$\lim _{x\to-2^+}g(x)=8.02$

From positive infinity, the closest value we can get to before -2 is -1.999 according to the values given in the table. The value of g(x) from the table is:

$\lim _{x\to-2^-}g(x)=8.03$

From the options, the closest estimate for the limit is 8.03.

The correct option is the SECOND OPTION.