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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{2}

\frac{d}{d x} (2 cos (x) + 2 x sin (x))

\frac{d y}{d x} + y = 2 x^{2}

\int (4 x + 5) d x

\frac{d}{d x} (arcsin (\frac{1}{x ^{5}}))

(1 - e^{z}) (z + e^{z})

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