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3 years ago

Hello quick question because i am dumb and dont know how to explain things just need some clarification

Mathematics

2 answers:

Strike441 [17]3 years ago

8 0

Step-by-step explanation:

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marissa [1.9K]3 years ago

4 0

9514 1404 393

Answer:

The domain is always discrete when it is found from a table.

Step-by-step explanation:

A table necessarily lists a finite number of discrete points. The domain, as found from a table, is always discrete.

If the table is said to be a representation of a continuous function, then the domain of that continuous function will be continuous.

Your question seems to have to do with a table alone, not a table and an equation, or a table and a graph. A table (of points) alone cannot express a continuous domain.

Additional comments

One can conceive of tables that would have continuous domains, as, for example, a table with entries ...

(x, y) = (0 ≤ x < 3, 3x+2), (3 ≤ x < 6, 4x-1), ...

Such a table is not a list of points, but is a piecewise function definition. We presume this is not what you're concerned with.

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The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

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Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

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And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

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If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

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Answer:

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