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

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

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

x \to 0 lim (∣ x ∣ cos (\frac{π}{x}))

0

Solution steps

x \to 0 lim (∣ x ∣ cos (\frac{π}{x}))

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

then

x \to a lim f (x) = L

x \to 0 - lim (∣ x ∣ cos (\frac{π}{x})) = 0

x \to 0 + lim (∣ x ∣ cos (\frac{π}{x})) = 0

= 0

x \to 0 - lim (\frac{9 sin ( x )}{x})

θ \to \frac{π}{6} lim (\frac{sin ( 2 θ )}{sin ( θ ) tan ( θ )})

x \to \infty lim (40)

x \to 2 - lim (ln (4 - x^{2}))

x \to 0 lim (x^{2} cos (\frac{π}{x}))

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