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

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

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

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

\frac{1}{8}

Decimal

0.125

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

cos (8 \cdot 0) \cdot 8 = 8

= \frac{1}{8}

x \to 1 lim (e^{x - 1} + 1)

\frac{\partial}{\partial x} (x ln (z^{7} + x^{4}))

y = x^{2} - 4 x - 3, (3, - 6)

(\frac{1}{x}), (\frac{1}{x ^{2}}), 2

y = 4 x^{2} + 3 y^{2} + 8 x - 6 y - 45, (- 2, - 3)

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