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

The limit as x approaches 0 of (sin(x))/(8x+tan(x)) is 1/9

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

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

\frac{1}{9}

Decimal Notation

0.11111 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( x )}{8 + sec ^{2} ( x )})

= x \to 0 lim (\frac{cos ( x )}{8 + sec ^{2} ( x )})

Plug in the value

x = 0

= \frac{cos ( 0 )}{8 + sec ^{2} ( 0 )}

Simplify

\frac{cos ( 0 )}{8 + sec ^{2} ( 0 )} : \frac{1}{9}

= \frac{1}{9}

x \to 3 - lim ((4 x) - 3 x)

x \to in f ini t e lim (\frac{1}{x})

x \to 3 lim (x^{2} - 5 x + 4)

x \to 1 lim (3 x^{2} - 4)

x \to - \infty lim (- x^{4})

What is the limit as x approaches 0 of (sin(x))/(8x+tan(x)) ?
The limit as x approaches 0 of (sin(x))/(8x+tan(x)) is 1/9