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 )})

Simplify

\frac{x}{sin ( - x )} : - x csc (x)

= x \to 0 lim (- x csc (x))

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

= - x \to 0 lim (x csc (x))

Rewrite for L'Hopital

= - x \to 0 lim (\frac{x}{\frac{1}{c s c ( 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 1 lim (\frac{7 x - 7}{8 x - 8})

x \to 0 lim (x^{2} \cdot ln ∣ x ∣)

x \to - 3 + lim (h (x))

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

x \to 0 lim (x^{2} - 9)

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