What is the limit as x approaches 0 of (2x)/(sin(x)) ?

The limit as x approaches 0 of (2x)/(sin(x)) is 2

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limit as x approaches 0 of (2x)/(sin(x))

x \to 0 lim (\frac{2 x}{sin ( x )})

2

Solution steps

x \to 0 lim (\frac{2 x}{sin ( x )})

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

= 2 \cdot x \to 0 lim (\frac{x}{sin ( x )})

Apply L'Hopital's Rule

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

= 2 \cdot x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 2 \cdot \frac{1}{cos ( 0 )}

Simplify

2 \cdot \frac{1}{cos ( 0 )} : 2

= 2

\int \frac{60 x ^{2} + 20 x}{10 x ^{3} + 5 x ^{2} + 3} d x

y = x x

\int \frac{1}{( x ^{2} + 64 ) ^{2}} d x

\frac{d}{d x} (e^{\frac{x}{10}})

x \to o - lim (4)

What is the limit as x approaches 0 of (2x)/(sin(x)) ?
The limit as x approaches 0 of (2x)/(sin(x)) is 2