Question

Review the table of values for function h(x).

x h(x)
8.9 3.83
8.99 –1.19
8.999 4.73
9 undefined
9.001 –4.73
9.01 1.19
9.1 –3.83
Which statement correctly explains whether Limit of h (x) as x approaches 9 exists?

The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9.
The limit does exist because h(x) is defined for all given values around x = 9, even though h(x) isn’t defined at x = 9.
The limit does not exist because h(x) is not defined at x = 9, and for a limit to exist, the function must be defined at x = 9.
The limit does exist because the values of h(x) to the right of x = 9 are all opposites of the values of h(x) to the left of x = 9.

Answer 1

Using lateral limits, the correct option is:

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

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For a limit of a function f(x) to exist at a point a, it is needed that:

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

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

These limits found, approaching a from close but smaller values, $[tex]\lim_{x\rightarrow a^-} f(x)$, and from close but greater values, $\lim_{x\rightarrow a^+} f(x)$, are called lateral limits.

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• From the table, looking at the value slightly less than 9, it can be said that: $\lim_{x \rightarrow 9^-} f(x) = 4.73$
• Looking at the value slightly more than 9, it can be said that: $\lim_{x \rightarrow 9^+} f(x) = -4.73$

Since the lateral limits are different, the limit does not exist, and the correct option is:

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

A similar question is given that https://brainly.com/question/23630768

Answer 2

Answer:

A

Step-by-step explanation: