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

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

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limit as x approaches 0 of (sin(8x))/(tan(9x))

x \to 0 lim (\frac{sin ( 8 x )}{tan ( 9 x )})

\frac{8}{9}

Decimal

0.88888 \dots

Solution steps

x \to 0 lim (\frac{sin ( 8 x )}{tan ( 9 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 8 x ) \cdot 8}{sec ^{2} ( 9 x ) \cdot 9})

= x \to 0 lim (\frac{cos ( 8 x ) \cdot 8}{sec ^{2} ( 9 x ) \cdot 9})

Plug in the value

x = 0

= \frac{cos ( 8 \cdot 0 ) \cdot 8}{sec ^{2} ( 9 \cdot 0 ) \cdot 9}

Simplify

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

= \frac{8}{9}

\int \frac{sin ( t )}{( 4 + cos ( t ) ) ^{5}} d t

\int (\frac{x}{x}) d x

4 x^{2}, 6 x - 2

\int \frac{2 x}{1 + x ^{2}} d x

\frac{\partial}{\partial x} (x e^{5 x y})

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