What is the limit as x approaches 0 of (sin(4x))/(tan(3x)) ?

The limit as x approaches 0 of (sin(4x))/(tan(3x)) is 4/3

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limit as x approaches 0 of (sin(4x))/(tan(3x))

x \to 0 lim (\frac{sin ( 4 x )}{tan ( 3 x )})

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

x \to 0 lim (\frac{sin ( 4 x )}{tan ( 3 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 4 x ) \cdot 4}{sec ^{2} ( 3 x ) \cdot 3})

= x \to 0 lim (\frac{cos ( 4 x ) \cdot 4}{sec ^{2} ( 3 x ) \cdot 3})

Plug in the value

x = 0

= \frac{cos ( 4 \cdot 0 ) \cdot 4}{sec ^{2} ( 3 \cdot 0 ) \cdot 3}

Simplify

\frac{cos ( 4 \cdot 0 ) \cdot 4}{sec ^{2} ( 3 \cdot 0 ) \cdot 3} : \frac{4}{3}

= \frac{4}{3}

\int_{1}^{\infty} 12 e^{- 6 x} d x

\frac{10 s ^{2}}{s ^{2} + 9}

x \to 1 lim (x^{2} + 5)

y^{^{'}} = x + 4 y - 2

\int (x - 3)^{- 2} d x

What is the limit as x approaches 0 of (sin(4x))/(tan(3x)) ?
The limit as x approaches 0 of (sin(4x))/(tan(3x)) is 4/3