What is the limit as x approaches 0 of cos((2pi)/x) ?

The limit as x approaches 0 of cos((2pi)/x) is diverges

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limit as x approaches 0 of cos((2pi)/x)

x \to 0 lim (cos (\frac{2 π}{x}))

diverges

Solution steps

x \to 0 lim (cos (\frac{2 π}{x}))

Apply Limit Divergence Criterion:

diverges

= diverges

x \to 0 lim (\frac{3 x}{∣ x ∣})

x \to 0 + lim (x^{- x})

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

x \to 3 lim (5 - 2 x)

x \to 4 lim (3 - 5 + x)

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