What is the limit as x approaches 0 of ((e^{3x}-1))/(sin(5x)) ?

The limit as x approaches 0 of ((e^{3x}-1))/(sin(5x)) is 3/5

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limit as x approaches 0 of ((e^{3x}-1))/(sin(5x))

x \to 0 lim (\frac{( e ^{3 x} - 1 )}{sin ( 5 x )})

\frac{3}{5}

Decimal

0.6

Solution steps

x \to 0 lim (\frac{e ^{3 x} - 1}{sin ( 5 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 e ^{3 x}}{cos ( 5 x ) \cdot 5})

= x \to 0 lim (\frac{3 e ^{3 x}}{cos ( 5 x ) \cdot 5})

Plug in the value

x = 0

= \frac{3 e ^{3 \cdot 0}}{cos ( 5 \cdot 0 ) \cdot 5}

Simplify

\frac{3 e ^{3 \cdot 0}}{cos ( 5 \cdot 0 ) \cdot 5} : \frac{3}{5}

= \frac{3}{5}

\int cos^{3} (x) sin^{3} (x) d x

y^{^{''}} - 81 y = 0

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\frac{2 x + 3}{3 x - 2}

\int (3 2 x + 1) d x

What is the limit as x approaches 0 of ((e^{3x}-1))/(sin(5x)) ?
The limit as x approaches 0 of ((e^{3x}-1))/(sin(5x)) is 3/5