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

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

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

x \to 0 lim (I n \frac{sin ( x )}{x})

n I

Solution steps

x \to 0 lim (I n \frac{sin ( x )}{x})

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= I n \frac{cos ( 0 )}{1}

Simplify

I n \frac{cos ( 0 )}{1} : n I

= n I

\frac{d}{d x} (4 x + \frac{600}{x} + 308)

y^{^{'}} + \frac{1}{x} y = \frac{7}{x ^{2}} + 3

x \to 1 lim (\frac{x - 3}{x ^{2} - 9})

\frac{d}{d x} (lo g_{4} (x^{2} - 9 x))

\int \frac{3}{- 1 - x} d x

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