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

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

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

x \to 0 lim (∣ x ∣ sin (\frac{1}{x}))

0

Solution steps

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

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

= 0

x \to - 1 lim (1 - x)

x \to 3 lim (x + 3)

x \to 1 + lim (x^{2} - x)

x \to \infty lim (x^{2} + 7 x + 2 - x)

x \to 0 + lim (ln (x) sin^{2} (x))

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