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

The limit as x approaches 0+of x*ln(sin(x)) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0+of x*ln(sin(x))

x \to 0 + lim (x \cdot ln (sin (x)))

0

Solution steps

x \to 0 + lim (x ln (sin (x)))

Rewrite for L'Hopital

= x \to 0 + lim (\frac{ln ( sin ( x ) )}{\frac{1}{x}})

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{cot ( x )}{- \frac{1}{x ^{2}}})

= x \to 0 + lim (\frac{cot ( x )}{- \frac{1}{x ^{2}}})

Simplify

= x \to 0 + lim (- x^{2} cot (x))

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

= - x \to 0 + lim (x^{2} cot (x))

Rewrite for L'Hopital

= - x \to 0 + lim (\frac{x ^{2}}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{2 x}{sec ^{2} ( x )})

= - x \to 0 + lim (\frac{2 x}{sec ^{2} ( x )})

Plug in the value

x = 0

= - \frac{2 \cdot 0}{sec ^{2} ( 0 )}

Simplify

- \frac{2 \cdot 0}{sec ^{2} ( 0 )} : 0

= 0

x \to \infty lim (1 - x^{4})

x \to 3 lim (9 - x^{22} x + 1)

x \to 0 - lim (π coth (\frac{1}{x}))

x \to 7 - lim (\frac{∣ x ∣ - x}{x - 7})

What is the limit as x approaches 0+of x*ln(sin(x)) ?
The limit as x approaches 0+of x*ln(sin(x)) is 0