What is the limit as x approaches 0 of (sin(x))/(8x) ?

The limit as x approaches 0 of (sin(x))/(8x) is 1/8

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limit as x approaches 0 of (sin(x))/(8x)

x \to 0 lim (\frac{sin ( x )}{8 x})

\frac{1}{8}

Decimal Notation

0.125

Solution steps

x \to 0 lim (\frac{sin ( x )}{8 x})

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

= \frac{1}{8} \cdot x \to 0 lim (\frac{sin ( x )}{x})

Apply L'Hopital's Rule

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

= \frac{1}{8} \cdot x \to 0 lim (\frac{cos ( x )}{1})

Plug in the value

x = 0

= \frac{1}{8} \cdot \frac{cos ( 0 )}{1}

Simplify

\frac{1}{8} \cdot \frac{cos ( 0 )}{1} : \frac{1}{8}

= \frac{1}{8}

f (x) = \frac{sin ( x ) + cos ( x )}{e ^{x}}

\int 3 x^{2} - 8 x + C d x

h (x) = (x tan (x))^{7}

\int x sin (a x) d x

\int ln (cos (x)) d x

What is the limit as x approaches 0 of (sin(x))/(8x) ?
The limit as x approaches 0 of (sin(x))/(8x) is 1/8