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 - \frac{π}{2} + lim (- 5 x - \frac{π}{2})

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

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

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

x \to \frac{π ^{+}}{2} lim (tan (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