Question

Which statement correctly explains whether Limit of h (x) as x approaches 9 exists?

Answer 1

Answer:

The answer is A

Step-by-step explanation:

"The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9" is correct edg 2021

Answer 2

The correct statement is "The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9".

What is a one-sided limit for function of a single variable?

In rough terminologies, the limit from one side is when we only use one side of the function with respect to the considered point of interest (in input) to predict the value of the function at that point.

For a limit of a function f(x) to exist at a point a,

$\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$

That is, it has to approach (a) from both sides toward the same value, thus it cannot be oscillating.

From the table, looking at the value of slightly less than 9,

$\lim_{x \to 9^-} f(x)= 4.73$

Looking at the value of slightly more than 9,

$\lim_{x \to 9^+} f(x) = -4.73$

Since the lateral limits are different, the limit does not exist.

The correct statement is "The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9".

Learn more about limits;

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