What is the limit as x approaches 0 of (4x)/(sin(x)) ?

The limit as x approaches 0 of (4x)/(sin(x)) is 4

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limit as x approaches 0 of (4x)/(sin(x))

x \to 0 lim (\frac{4 x}{sin ( x )})

4

Solution steps

x \to 0 lim (\frac{4 x}{sin ( x )})

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

= 4 \cdot x \to 0 lim (\frac{x}{sin ( x )})

Apply L'Hopital's Rule

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

= 4 \cdot x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 4 \cdot \frac{1}{cos ( 0 )}

Simplify

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

= 4

f (x) = 2 + \frac{7}{x} + \frac{2}{x ^{2}}

1 + tan^{2} (x)

\int (1 - csc (x) cot (x)) d x

\frac{d}{d x} (sin (2 x^{3} - 3))

x^{2} + 6 x

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