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

The limit as x approaches 0 of 1/(xsin(x)) is infinity

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limit as x approaches 0 of 1/(xsin(x))

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

\infty

Solution steps

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

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

= \infty

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

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

x \to - 2 + lim (\frac{1}{4 - x ^{2}})

x \to \infty lim (\frac{2 x + 5}{x ^{2} - 7 x + 3})

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

What is the limit as x approaches 0 of 1/(xsin(x)) ?
The limit as x approaches 0 of 1/(xsin(x)) is infinity