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zaharov [31]
3 years ago
10

Which statements are true? Select all that apply.

Mathematics
1 answer:
ohaa [14]3 years ago
5 0

Answer:

Two of these statements are true.

The function equals x^2 over the interval −∞ < x ≤ 0.

The function equals √x over the interval 0 ≤ x < ∞.

Step-by-step explanation:

If we look at the parent function of x^{2} we see that x^{2} function looks like a U shaped graph and in your graph we see it is the same as your graph from the interval (-∞,0).

If we look at the parent function of \sqrt{x}  we see that the

\sqrt{x} function looks like your graph from the interval (0,∞).

Suggestion:

I suggest memorizing every graph of parent functions that is introduced to you in math. This can help you visually with many problems in mathematics, and help you conceptualize material better. I also suggest looking up the definition of every word that may be unfamiliar to you like "interval" and "parent function". This will help you understand more advanced math notations and vocabulary in the future.

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Arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the fun
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Answer:

Following are the responses to the given question:

Step-by-step explanation:

When x is squared, it's going to be bigger by the conclusion because the larger the faster. x^2 + 4consistently exceeds 4 x^2, regardless of the price of X.

5x+3 is always 3 more so than 5x.

In particular, this can be classified according to its pathways (5x

 5x\\\\5x + 3\\\\7x\\\\8x + 3\\\\x^2\\\\x^2 + 4

So can alternatively just say "eventually," which means because when x really is big, you need to find one another's values. Then just select x=100, then plug it into every single other. To confirm this order:

5(100) = 500\\\\5(100) + 3 = 503\\\\7(100) = 700\\\\8(100) + 3 = 803\\\\(100)^2 = 10,000\\\\(100)^2 + 4 = 10,004\\\\

So, the ascending order must be the right order!

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2 years ago
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Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.
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Answer:

Step-by-step explanation:

Given the definite integral \int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx, we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}

= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} }  \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du }  \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}]  \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\

= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C

substitute u = 1-2x⁵ into the result

= \dfrac{1}{40(1-2x^5)^4} +C

Hence\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx = \dfrac{1}{40(1-2x^5)^4} +C

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