What is the limit as x approaches 0 of x/4 sin(1/x) ?

The limit as x approaches 0 of x/4 sin(1/x) is 0

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limit as x approaches 0 of x/4 sin(1/x)

x \to 0 lim (\frac{x}{4} sin (\frac{1}{x}))

0

Solution steps

x \to 0 lim (\frac{x}{4} sin (\frac{1}{x}))

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

= \frac{1}{4} \cdot x \to 0 lim (x sin (\frac{1}{x}))

Apply the Squeeze Theorem:

0

= \frac{1}{4} \cdot 0

Simplify

= 0

x \to \frac{π}{2} lim (2 cos (x))

h \to 0 lim ((1 + 4 h)^{\frac{1}{h}})

x \to 3 lim (\frac{e ^{x} - 1}{x})

x \to 0 lim (+ (x e^{\frac{1}{x}}))

x \to \infty lim ((x)^{0})

What is the limit as x approaches 0 of x/4 sin(1/x) ?
The limit as x approaches 0 of x/4 sin(1/x) is 0