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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Simplify

\frac{1}{x} sin (\frac{x}{2}) : \frac{sin ( \frac{x}{2} )}{x}

= x \to 0 lim (\frac{sin ( \frac{x}{2} )}{x})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{cos ( \frac{0}{2} ) \frac{1}{2}}{1}

Simplify

\frac{cos ( \frac{0}{2} ) \frac{1}{2}}{1} : \frac{1}{2}

= \frac{1}{2}

x \to 2 - lim (3 + ∣ 2 x - 4 ∣)

x \to 0 lim (1 - \frac{2}{x - 3})

x \to 0 lim (ln (1 + 2 x^{2}))

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

x \to 3 lim (15)

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