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

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

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

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

diverges

Solution steps

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

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

= diverges

x \to π lim (cos (6 x))

x \to - 4 lim (3 x + 10)

x \to 0 lim (\frac{1}{x \cdot cos ( x )})

x \to - 1 lim (x^{2} - 4 x + 5)

x \to a lim (2^{2 x})

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