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Blababa [14]
3 years ago
10

Please help! need answers in order to move on:) will give brainliest if you are correct!

Mathematics
1 answer:
shepuryov [24]3 years ago
5 0

Answer:

1) x^{2/3}

3 → index

\sqrt[3]{x^{2} }

Index: 3

<u>----------------</u>

2) 7^{5/4}

=\sqrt[4]{7^{5} }

=(\sqrt[4]{7})^{5}

<u>----------------</u>

3) \sqrt[7]{2^{3} }

=(2^{3} )^{1/7}  [\sqrt[x]{n} =n^{1/n} ]

=2^{3/7}

<u>----------------</u>

3) \sqrt[12]{8^{4} }

y=(8^{4} )^{1/12}

y=(8)^{1/3}

y=(2)^{3\times 1/3}

y=2

<u>------------------</u>

4) 128^{3/7}

=\sqrt[7]{2\times 2\times2\times 2\times 2\times2\times 2}

=(2)^{3}

=8

<u>----------------------</u>

<u>OAmalOHopeO</u>

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13d-(-9d-4)
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Find the derivative of f(x) = 12x^2 + 8x at x = 9.
zvonat [6]

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

(f+g)'=f'+g' Sum rule.

(cf)'=cf' Constant multiple rule.

(x^n)'=nx^{n-1} Power rule.

(x)'=1 Slope of y=x is 1.

f(x)=12x^2+8x

f'(x)=(12x^2+8x)'

f'(x)=(12x^2)'+(8x)' by sum rule.

f'(x)=12(x^2)+8(x)' by constant multiple rule.

f'(x)=12(2x)+8(1) by power rule.

f'(x)=24x+8

Now we need to find the derivative function evaluated at x=9.

f'(9)=24(9)+8

f'(9)=216+8

f'(9)=224

In case you wanted to use the formal definition of derivative:

f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}

Or the formal definition evaluated at x=a:

f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}

Let's use that a=9.

f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}

We need to find f(9+h) and f(9):

f(9+h)=12(9+h)^2+8(9+h)

f(9+h)=12(9+h)(9+h)+72+8h

f(9+h)=12(81+18h+h^2)+72+8h

(used foil or the formula  (x+a)(x+a)=x^2+2ax+a^2)

f(9+h)=972+216h+12h^2+72+8h

Combine like terms:

f(9+h)=1044+224h+12h^2

f(9)=12(9)^2+8(9)

f(9)=12(81)+72

f(9)=972+72

f(9)=1044

Ok now back to our definition:

f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}

f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}

Simplify by doing 1044-1044:

f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}

Each term has a factor of h so divide top and bottom by h:

f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}

f'(9)=\lim_{h \rightarrow 0}(224+12h)

f'(9)=224+12(0)

f'(9)=224+0

f'(9)=224

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3 years ago
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Answer:

No

Step-by-step explanation:

Hope it helps......

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4 years ago
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Taya2010 [7]

Answer:

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Step-by-step explanation:

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32=4x+4

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