What is the limit as x approaches 0 of (e^x-1)/(sin(4x)) ?

The limit as x approaches 0 of (e^x-1)/(sin(4x)) is 1/4

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limit as x approaches 0 of (e^x-1)/(sin(4x))

x \to 0 lim (\frac{e ^{x} - 1}{sin ( 4 x )})

\frac{1}{4}

Decimal

0.25

Solution steps

x \to 0 lim (\frac{e ^{x} - 1}{sin ( 4 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{e ^{x}}{cos ( 4 x ) \cdot 4})

= x \to 0 lim (\frac{e ^{x}}{cos ( 4 x ) \cdot 4})

Plug in the value

x = 0

= \frac{e ^{0}}{cos ( 4 \cdot 0 ) \cdot 4}

Simplify

\frac{e ^{0}}{cos ( 4 \cdot 0 ) \cdot 4} : \frac{1}{4}

= \frac{1}{4}

e^{- t} sin (t)

\frac{\partial}{\partial x} (6 y - 2 x)

- \frac{3}{x ^{4}}

y = 25 - x^{2}, (3, 4)

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

What is the limit as x approaches 0 of (e^x-1)/(sin(4x)) ?
The limit as x approaches 0 of (e^x-1)/(sin(4x)) is 1/4