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

The limit as x approaches 0+of xln(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 xln(sin(x))

x \to 0 + lim (x 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

\int \frac{1}{5 x - 2} d x

\int \frac{1}{( 1 + u ) ^{2}} d u

\frac{d r}{d θ} = 8 (cos (\frac{θ}{3}))^{3}

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

y^{^{''}} + 10 y^{^{'}} + 2500 = 500 sin (100 x)

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