The correct option is B ∞ When x→ 2 / 5 | 5x 2 | #160; =5x 2 So, lim _ x→ 2 / 5 #160; 1/5x 2 #160; #160; Substituting x = ...

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Definition of Relations

limx→2/51/ | ...

Question

$lim x \to \frac{2}{5} \frac{1}{| 5 x - 2 |}$ =_____

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\infty

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Does not exist

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Solution

The correct option is B $\infty$
When $x \to \frac{2}{5}$
$| 5 x - 2 | = 5 x - 2$
So, $lim x \to \frac{2}{5} \frac{1}{5 x - 2}$
Substituting $x = \frac{2}{5}$ , we get
$= \frac{1}{5 (\frac{2}{5}) - 2} = \frac{1}{2 - 2} = \frac{1}{0} = \infty$

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