What is the limit as x approaches 0 of (sin(3x))/(e^{2x)-1} ?

The limit as x approaches 0 of (sin(3x))/(e^{2x)-1} is 3/2

Popular >

limit as x approaches 0 of (sin(3x))/(e^{2x)-1}

x \to 0 lim (\frac{sin ( 3 x )}{e ^{2 x} - 1})

\frac{3}{2}

Decimal

1.5

Solution steps

x \to 0 lim (\frac{sin ( 3 x )}{e ^{2 x} - 1})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{3}{2}

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

x \to 3 - lim (\frac{x + 2}{x - 3})

x \to - 4 lim ((10 + 4)^{2})

x \to - \frac{3 π}{2} lim (tan (x))

x \to 0 lim (tan (x^{x}))

What is the limit as x approaches 0 of (sin(3x))/(e^{2x)-1} ?
The limit as x approaches 0 of (sin(3x))/(e^{2x)-1} is 3/2