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

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

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

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

diverges

Solution steps

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

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

then the limit does not exist

x \to 0 + lim (\frac{cos ( x ) - cos ( 3 x )}{x ^{3}}) = \infty

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

= diverges

x \to 0 lim (6 sin (x))

x \to 2 lim (x^{5} + 2 x^{3} - x - 8)

x \to 0 + lim (x - 1)

x \to 3 lim (4 x - 6)

x \to 0 lim (cos (- x))

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