What is the limit as x approaches 0+of xcos(pi/x) ?

The limit as x approaches 0+of xcos(pi/x) is 0

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limit as x approaches 0+of xcos(pi/x)

x \to 0 + lim (x cos (\frac{π}{x}))

0

Solution steps

x \to 0 + lim (x cos (\frac{π}{x}))

Apply the Squeeze Theorem:

0

= 0

x \to \infty lim (\frac{1. 1 ^{x}}{x})

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

x \to \frac{4}{5} lim (\frac{1}{5 x - 4})

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

x \to 3 lim (\frac{3 x ^{2} + 5 x + 1}{x})

What is the limit as x approaches 0+of xcos(pi/x) ?
The limit as x approaches 0+of xcos(pi/x) is 0