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The graph of the function h is shown.

piecewise graph of h of x equals cosine of log x over x where x is less than or equal to 1, 1 tenth over the quantity x plus 1 all squared minus 1 and 1 tenth where x is greater than or equal to negative 2 and less than 0, negative quantity x plus 3 all squared plus 2 where x is less than negative 2

Why is the limit of h of x as x approaches negative 2 nonexistent? (6 points)
The limit is unbounded.
The limit from the left does not equal the limit from the right.
The limit is oscillating around the x‒value.
The x‒value is approaching the endpoint of an interval.

The graph of the function h is shown. piecewise graph of h of x equals cosine of log x over x where x is less than or equal to 1, 1 tenth over the quantity x pl class=

Answer :

azikennamdi

The limit of h(x) is nonexistent because "the limit is unbounded" (Option A)

What is an unbounded limit?

When we graph the given function, we can observe that h(x) rises without bound when x approaches 0 on either the right or left side.

This indicates that if we select an x number near to zero, we will get h(x) to be as huge as we wish. As a result, the limit does not exist in this case.

It is worth noting that as we get closer and closer to 0 from the right, the values for one over x squared without bound grow greater and larger.

So language that people will sometimes use, when they're both traveling in the same way but it's unbounded, is "this limit is unbounded."

Hence, the correct answer is option A.

Learn more about unbounded limit:
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