What is the limit as x approaches 0 of ln(sin(|x|)) ?

The limit as x approaches 0 of ln(sin(|x|)) is -infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 0 of ln(sin(|x|))

x \to 0 lim (ln (sin (∣ x ∣)))

- \infty

Solution steps

x \to 0 lim (ln (sin (∣ x ∣)))

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (ln (sin (∣ x ∣))) = - \infty

x \to 0 + lim (ln (sin (∣ x ∣))) = - \infty

= - \infty

x \to - 2 lim (2 \frac{x}{x ^{2} - 4})

x \to - \infty lim (e^{x} - 2)

x \to 0 lim (\frac{3 ^{2 x} - 1}{x})

x \to - 1 lim (1 - 4 x)

x \to - \infty lim (2^{x} - 1)

What is the limit as x approaches 0 of ln(sin(|x|)) ?
The limit as x approaches 0 of ln(sin(|x|)) is -infinity