What is the limit as x approaches 0 of 1/(sin(4x)) ?

The limit as x approaches 0 of 1/(sin(4x)) is diverges

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limit as x approaches 0 of 1/(sin(4x))

x \to 0 lim (\frac{1}{sin ( 4 x )})

diverges

Solution steps

x \to 0 lim (\frac{1}{sin ( 4 x )})

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

then the limit does not exist

x \to 0 + lim (\frac{1}{sin ( 4 x )}) = \infty

x \to 0 - lim (\frac{1}{sin ( 4 x )}) = - \infty

= diverges

θ \to 0 lim (θ sin (θ))

x \to 3 lim (x^{2} e^{x} - sin (x))

x \to 0 lim (5132)

x \to 2 lim (\frac{x}{∣ 2 - x ∣})

x \to 8 lim (8)

What is the limit as x approaches 0 of 1/(sin(4x)) ?
The limit as x approaches 0 of 1/(sin(4x)) is diverges