Limits q (1 Viewer)

photastic · Mar 24, 2015

InteGrand · Mar 24, 2015

photastic said:

$\left | \frac{-3x+7}{7x+7}+\frac{3}{7} \right| <0.01\Leftrightarrow \left | \frac{-3x+7+3(x+1)}{7x+7} \right| <0.01$ (taking a common denominator)

$\Leftrightarrow \left | \frac{10}{7(x+1)} \right| <0.01$

$\Leftarrow \frac{10}{7(x+1)}<\frac{1}{100}, x>0, \text{ say}$

$\Leftarrow \frac{10}{7x}<\frac{1}{100}$

$\Leftrightarrow x>\frac{1000}{7}$ , so $M = \frac{1000}{7}$ works.

photastic · Mar 24, 2015

InteGrand said:
$\left | \frac{-3x+7}{7x+7}+\frac{3}{7} \right| <0.01\Leftrightarrow \left | \frac{-3x+7+3(x+1)}{7x+7} \right| <0.01$ (taking a common denominator)

$\Leftrightarrow \left | \frac{10}{7(x+1)} \right| <0.01$

$\Leftarrow \frac{10}{7(x+1)}<\frac{1}{100}, x>0, \text{ say}$

$\Leftarrow \frac{10}{7x}<\frac{1}{100}$

$\Leftrightarrow x>\frac{1000}{7}$ , so $M = \frac{1000}{7}$ works.

Why did 7(x+1) change into 7x?

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Limits q (1 Viewer)

photastic

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InteGrand

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photastic

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