What is the limit as x approaches 0 of sin(|x|)(1/x) ?

The limit as x approaches 0 of sin(|x|)(1/x) is diverges

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limit as x approaches 0 of sin(|x|)(1/x)

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

diverges

Solution steps

x \to 0 lim (sin (∣ x ∣) \frac{1}{x})

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

then the limit does not exist

x \to 0 + lim (sin (∣ x ∣) \frac{1}{x}) = 1

x \to 0 - lim (sin (∣ x ∣) \frac{1}{x}) = - 1

= diverges

x \to - 4 lim (g (x))

x \to 3 lim (x (3))

x \to 0 lim (x^{2} [\frac{1}{x ^{2}}])

x \to \infty lim (x + x^{2})

x \to \infty lim (e^{x} x^{2})

What is the limit as x approaches 0 of sin(|x|)(1/x) ?
The limit as x approaches 0 of sin(|x|)(1/x) is diverges