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

The limit as x approaches 0 of-x/(sin(x)) is -1

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

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

- 1

Solution steps

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

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= - \frac{1}{cos ( 0 )}

Simplify

- \frac{1}{cos ( 0 )} : - 1

= - 1

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

x \to \infty lim (\frac{x}{π})

x \to - 2 lim (3 x + 5)

x \to - 2 lim (3 x + 1)

x \to - 2 lim (3 x - 4)

What is the limit as x approaches 0 of-x/(sin(x)) ?
The limit as x approaches 0 of-x/(sin(x)) is -1