lim_x→251|5x 2| As |5x 2| ≥ 0 , the given limit exists.Therefore, lim_x→251|5x 2|=10=∞ ...

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Algebra of Limits

limx→251|5x-2...

Question

$l i m_{x \to \frac{2}{5}} \frac{1}{| 5 x - 2 |}$

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Solution

$l i m_{x \to \frac{2}{5}} \frac{1}{| 5 x - 2 |}$

As $| 5 x - 2 | \geq 0$ , the given limit exists.
Therefore,
$l i m_{x \to \frac{2}{5}} \frac{1}{| 5 x - 2 |} = \frac{1}{0} = \infty$

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