What is the limit as x approaches 0 of (3x)/(sin(10x)) ?

The limit as x approaches 0 of (3x)/(sin(10x)) is 3/10

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limit as x approaches 0 of (3x)/(sin(10x))

x \to 0 lim (\frac{3 x}{sin ( 10 x )})

\frac{3}{10}

Decimal Notation

0.3

Solution steps

x \to 0 lim (\frac{3 x}{sin ( 10 x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to 0 lim (\frac{x}{sin ( 10 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{cos ( 10 x ) \cdot 10})

= 3 \cdot x \to 0 lim (\frac{1}{cos ( 10 x ) \cdot 10})

Plug in the value

x = 0

= 3 \cdot \frac{1}{cos ( 10 \cdot 0 ) \cdot 10}

Simplify

3 \cdot \frac{1}{cos ( 10 \cdot 0 ) \cdot 10} : \frac{3}{10}

= \frac{3}{10}

\frac{\partial}{\partial x} (3 (y - 1)^{3} (x - 6))

\int \frac{x ^{3}}{x ^{2} + 4 x + 4} d x

\int (x - 1)^{2} - 4 d x

\int (x + 1) (x + 2) d x

x \to 1 lim (\frac{1}{x + 1})

What is the limit as x approaches 0 of (3x)/(sin(10x)) ?
The limit as x approaches 0 of (3x)/(sin(10x)) is 3/10