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vlada-n [284]
3 years ago
11

Calculus Help Show that one function is not an antiderivative of another

Mathematics
1 answer:
liraira [26]3 years ago
6 0

Just differentiate <em>G</em> and <em>H</em> :

• d<em>G</em>/d<em>x</em> = d(<em>x</em> ² <em>eˣ </em>)/d<em>x</em> = 2<em>x</em> <em>eˣ</em> + <em>x</em> ² <em>eˣ</em>

so <em>G</em> is not an antiderivative of <em>f</em>.

• d<em>H</em>/d<em>x</em> = d(2<em>x</em> <em>eˣ</em> - 2<em>eˣ</em> ) = (2<em>eˣ</em> + 2<em>x</em> <em>eˣ</em> ) - 2<em>eˣ</em> = 2<em>x</em> <em>eˣ</em> = <em>f(x)</em>

so <em>H</em> is indeed an antiderivative of <em>f</em>.

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Akimi4 [234]

Answer:

As we know:

Direct variation => y = k*x, k is constant ( y/x = k = constant)

Inverse variation => y = k/x, k is constant (y*x = k = constant)

X - 1 2 5 10

Y - 6 12 30 60

Check the first 2 pair of X, Y:

(the remaining pair of value would show the same tendency)

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=> B and D is incorrect

Otherwise, we have:

Y1/X1 = 6/1 = 6

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=> Y/X = 6

=> A direct variation with k = 6

=> y = 6x

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3 years ago
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Nonamiya [84]

Answer:

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Step-by-step explanation:

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6/8 = n/12

Step-by-step explanation:

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Answer:

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<u><em>The equation is y = (1/2)x + - 3.5</em></u>

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