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Sagot :
Using limits, it is found that the end behavior of the polynomial function for the volume of the rectangular box is:
B. down and up.
What is the volume of a rectangular prism?
The volume of a rectangular prism of length l, width w and heigth h is given by:
V = lwh.
In this problem, we have that the dimensions are given by:
- w = x.
- l = x - 1.
- h = x - 2.
Hence the volume is given by:
[tex]V = x(x - 1)(x - 2) = x(x^2 - 3x + 2) = x^3 - 3x^2 + 2x[/tex]
What is the end behavior of a function?
It is given by it's limits as x goes to infinity.
Hence:
[tex]\lim_{x \rightarrow -\infty} V(x) = \lim_{x \rightarrow -\infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow -\infty} x^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} V(x) = \lim_{x \rightarrow \infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow \infty} x^3 = \infty[/tex]
Which means that option B is correct.
More can be learned about limits at brainly.com/question/22026723
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