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Aleks04 [339]
3 years ago
10

Simplify the exponential expression. (−8) 2 =

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
6 0

Answer:

-16

Step-by-step explanation:

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Computing the limit directly:

\displaystyle\lim_{h\to0}\frac{f(2+h)-f(2)}h=\lim_{h\to0}\frac{((2+h)^2+(2+h)+1)-7}h\\\displaystyle=\lim_{h\to0}\frac{5h+h^2}h\\=\displaystyle\lim_{h\to0}(5+h)=\boxed{5}

Alternatively, you can recognize the limit as being equivalent the derivative of <em>f(x)</em> at <em>x</em> = 2, in which case differentiating and plugging in 2 gives

<em>f'(x)</em> = 2<em>x</em> + 1   =>   <em>f'</em> (2) = 5

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