What is the limit as x approaches 0+of (9x)/(|x|) ?

The limit as x approaches 0+of (9x)/(|x|) is 9

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limit as x approaches 0+of (9x)/(|x|)

x \to 0 + lim (\frac{9 x}{∣ x ∣})

9

Solution steps

x \to 0 + lim (\frac{9 x}{∣ x ∣})

x

is positive when

x \to 0 +

. Therefore

∣ x ∣ = x

= x \to 0 + lim (\frac{9 x}{x})

Cancel the common factor:

x

= x \to 0 + lim (9)

x \to a lim c = c

= 9

x \to 0 lim (\frac{3 x}{2 x})

x \to 0 - lim (x e^{x})

x \to 2 lim (e^{\frac{x}{x - 2}})

x \to 0 lim (\frac{1 - e ^{x}}{3 x})

x \to 0 lim (2 sin (\frac{1}{x}))

What is the limit as x approaches 0+of (9x)/(|x|) ?
The limit as x approaches 0+of (9x)/(|x|) is 9