What is the limit as x approaches 0 of x/2 cos(1/x) ?

The limit as x approaches 0 of x/2 cos(1/x) is 0

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limit as x approaches 0 of x/2 cos(1/x)

x \to 0 lim (\frac{x}{2} cos (\frac{1}{x}))

0

Solution steps

x \to 0 lim (\frac{x}{2} cos (\frac{1}{x}))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{2} \cdot x \to 0 lim (x cos (\frac{1}{x}))

Apply the Squeeze Theorem:

0

= \frac{1}{2} \cdot 0

Simplify

= 0

x \to \infty lim (- 2, x)

x \to 1 lim (3 x^{2} - 7 x)

x \to 3 + lim (\frac{9}{( x - 3 ) ^{5}})

x \to 2 - lim (e^{\frac{5}{2 - x}})

x \to 0 lim (- 2 x ln (x))

What is the limit as x approaches 0 of x/2 cos(1/x) ?
The limit as x approaches 0 of x/2 cos(1/x) is 0