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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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 \infty lim ((1 + x)^{\frac{2}{x}})

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = 3

\int_{0}^{2} 5 d x

\frac{\partial}{\partial x} (x y^{9} - x^{2} y)

x \to 6 lim (x^{2} + 13)

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