Kyle needs to build a crate in the shape of a rectangular prism. The crate must have a volume of 160 cubic feet, and a height of
1 answer:
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Answer:
volume V of the solid
Step-by-step explanation:
The situation is depicted in the picture attached
(see picture)
First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each
[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]
Now, we slice our solid into n slices.
Each slice is a quarter of cylinder 5/n thick and has a radius of
-k(5/n) + 5 for each k = 1,2,..., n (see picture)
So the volume of each slice is
for k=1,2,..., n
We then add up the volumes of all these slices
Notice that the last term of the sum vanishes. After making up the expression a little, we get
But
we also know that
and
so we have, after replacing and simplifying, the sum of the slices equals
Now we take the limit when n tends to infinite (the slices get thinner and thinner)
and the volume V of our solid is
Answer:
As x —> negative infinity, f(x) —> negative infinity
As x —> positive infinity, f(x) —> positive infinity.
Step-by-step explanation:
An odd-degree function, meaning that the graph starts from negative infinity at x —> negative infinity and positive infinity at x —> positive infinity.
As x —> negative infinity, f(x) —> negative infinity
As x —> positive infinity, f(x) —> positive infinity.
An odd-degree function is an one-to-one function so whenever x approaches positive, f(x) will also approach positive.