Using translation concepts, it is found that the correct option regarding the function is:
The function h(x) is decreasing on the interval (3, ∞).
<h3>What is a translation?</h3>A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
Which increases on (0, ∞).
The translated function is given by:
With the translation, the domain is now (-3, ∞), and the function is decreasing, hence the correct option is given by:
The function h(x) is decreasing on the interval (3, ∞).
More can be learned about translation concepts at brainly.com/question/4521517
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Expand everything in the limit:
We have approaching 0, and in particular
, so we can cancel a factor in the numerator and denominator:
Alternatively, if you already know about derivatives, consider the function , whose derivative is
.
Using the limit definition, we have
which is exactly the original limit with . The derivative is
, so the value of the limit is, again, -14.