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

\frac{d y}{d x} - y = e^{x} y^{2}

(- 17, - 5), (2, - 18)

y = (7 x - 1)

lo g_{8} (x)

\int \frac{3 x ^{2} - 2 x + 5}{( x + 3 ) ^{3}} d 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