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3 years ago

Which choice is the answer

Mathematics

1 answer:

Montano1993 [528]3 years ago

5 0

The answer would be D.

a1 is 0.5 and r is -0.2.

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vaieri [72.5K]

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Solve each system of equation algebraically<br> Y=x+12<br> Y=-18

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3 years ago

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Answer:

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4 years ago

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liubo4ka [24]

Answer: $-\frac{9}{x^2}$

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Work Shown:

$\displaystyle \lim_{\Delta x \to 0^{+}} \frac{\frac{9}{x+\Delta x} - \frac{9}{x}}{\Delta x}\\\\\\\displaystyle \lim_{\Delta x \to 0^{+}} \frac{\frac{9x}{x(x+\Delta x)} - \frac{9(x+\Delta x)}{x(x+\Delta x)}}{\Delta x}\\\\\\\displaystyle \lim_{\Delta x \to 0^{+}} \frac{\frac{9x-9(x+\Delta x)}{x(x+\Delta x)}}{\Delta x}\\\\\\\displaystyle \lim_{\Delta x \to 0^{+}} \frac{9x-9x-9\Delta x}{x\Delta x(x+\Delta x)}\\\\\\$

$\displaystyle \lim_{\Delta x \to 0^{+}} \frac{-9\Delta x}{x\Delta x(x+\Delta x)}\\\\\\\displaystyle \lim_{\Delta x \to 0^{+}} \frac{-9}{x(x+\Delta x)}\\\\\\\displaystyle \frac{-9}{x(x+0)}\\\\\\\displaystyle -\frac{9}{x^2}\\\\\\$

The trick here is to first simplify the expression so that the $\Delta x$ term in the very lower denominator cancels out. This is to avoid dividing by zero. Once this division by zero error is avoided, we can replace the delta x term with 0 and evaluate the limit as $\Delta x$ approaches 0 from the right or positive direction.

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3 years ago