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Vaselesa [24]
3 years ago
15

Exercise 2.11

Mathematics
1 answer:
yan [13]3 years ago
5 0
\int 8\, dx=8x+C\\\\
0=8\cdot1+C\\
C=-8\\
f'(x)=8x-8\\\\
\int 8x-8\, dx=4x^2-8x+C\\\\
3=4\cdot1^2-8\cdot1+C\\
3=4-8+C\\
C=7\\\\
\boxed{f(x)=4x^2-8x+7}

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Step-by-step explanation:

Hello,

This is the same method as computing for instance:

\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}

We need to find the same denominator.

Let's do it !

For any x real different from 0, we can write:

\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}

Hope this helps.

Do not hesitate if you need further explanation.

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