What is the limit as x approaches 0 of (2/3 cos(x)-1)/x ?

The limit as x approaches 0 of (2/3 cos(x)-1)/x is diverges

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limit as x approaches 0 of (2/3 cos(x)-1)/x

x \to 0 lim (\frac{\frac{2}{3} cos ( x ) - 1}{x})

diverges

Solution steps

x \to 0 lim (\frac{\frac{2}{3} cos ( x ) - 1}{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{\frac{2}{3} cos ( x ) - 1}{x}) = - \infty

x \to 0 - lim (\frac{\frac{2}{3} cos ( x ) - 1}{x}) = \infty

= diverges

x \to 0 lim (\frac{e ^{x} - 1}{5 x ^{2}})

x \to 0 lim (\frac{\frac{1}{x ^{2}}}{e ^{\frac{1}{x ^{2}}}})

x \to 0 lim (x^{8})

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

x \to 0 + lim (tan (x ln (x)))

What is the limit as x approaches 0 of (2/3 cos(x)-1)/x ?
The limit as x approaches 0 of (2/3 cos(x)-1)/x is diverges