What is the limit as x approaches 0 of x/(|x|)sin(x) ?

The limit as x approaches 0 of x/(|x|)sin(x) is 0

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limit as x approaches 0 of x/(|x|)sin(x)

x \to 0 lim (\frac{x}{∣ x ∣} sin (x))

0

Solution steps

x \to 0 lim (\frac{x}{∣ x ∣} sin (x))

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (\frac{x}{∣ x ∣} sin (x)) = 0

x \to 0 + lim (\frac{x}{∣ x ∣} sin (x)) = 0

= 0

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What is the limit as x approaches 0 of x/(|x|)sin(x) ?
The limit as x approaches 0 of x/(|x|)sin(x) is 0