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Kaylis [27]
2 years ago
7

Distribute to write an equivalent expression. 2n * (n ^ 2 + 3n + 4)

Mathematics
1 answer:
OverLord2011 [107]2 years ago
6 0

Answer:

C. 2n^3 + 6n^2 + 8n

Explanation:

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Limit definition for slope of the graph, equation of tangent line point for<br> f(x)=2x^2 at x=(-1)
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The slope of the tangent line to f at x=-1 is given by the derivative of f at that point:

f'(-1)=\displaystyle\lim_{x\to-1}\frac{f(x)-f(-1)}{x-(-1)}=\lim_{x\to-1}\frac{2x^2-2}{x+1}

Factorize the numerator:

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We have x approaching -1; in particular, this means x\neq-1, so that

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

Then

f'(-1)=\displaystyle\lim_{x\to-1}\frac{2x^2-2}{x+1}=\lim_{x\to-1}2(x-1)=2(-1-1)=-4

and the tangent line's equation is

y-f(-1)=f'(-1)(x-(-1))\implies y-4x-2

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