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

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

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

x \to 0 lim (sin (\frac{1}{∣ x ∣}))

diverges

Solution steps

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

diverges

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

diverges

= diverges

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\int (cos^{2} (x)) d x

\int (2^{x}) d x

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