What is the limit as x approaches 0 of ((sin(8x)))/(3x) ?

The limit as x approaches 0 of ((sin(8x)))/(3x) is 8/3

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limit as x approaches 0 of ((sin(8x)))/(3x)

x \to 0 lim (\frac{( sin ( 8 x ) )}{3 x})

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

x \to 0 lim (\frac{sin ( 8 x )}{3 x})

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

= \frac{1}{3} \cdot x \to 0 lim (\frac{sin ( 8 x )}{x})

Apply L'Hopital's Rule

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

= \frac{1}{3} \cdot x \to 0 lim (\frac{cos ( 8 x ) \cdot 8}{1})

Plug in the value

x = 0

= \frac{1}{3} \cdot \frac{cos ( 8 \cdot 0 ) \cdot 8}{1}

Simplify

\frac{1}{3} \cdot \frac{cos ( 8 \cdot 0 ) \cdot 8}{1} : \frac{8}{3}

= \frac{8}{3}

\frac{d}{d x} (cos (3 x + 3))

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

cos (x^{2}) \cdot 2 x

16

\frac{d}{d x} (e^{t a n (x^{3})})

What is the limit as x approaches 0 of ((sin(8x)))/(3x) ?
The limit as x approaches 0 of ((sin(8x)))/(3x) is 8/3