First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{3 x + | x |}{7 x - | x |}$ , is

Moderate

A

2
B

$\frac{1}{6}$
C

0
D

does not exist

Solution

We have,
$lim_{x \to 0^{-}} \frac{3 x + | x |}{7 x - 5 | x |} = lim_{x \to 0} \frac{3 x - x}{7 x + 5 x} = \frac{1}{6}$
and, $lim_{x \to 0^{+}} \frac{3 x + | x |}{7 x - 5 | x |} = lim_{x \to 0} \frac{3 x + x}{7 x - 5 x} = 2$
So, $lim_{x \to 0} \frac{3 x + | x |}{7 x - 5 | x |}$ does not exist.

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