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

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

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/(arcsin(x))

x \to 0 lim (\frac{x}{arcsin ( x )})

1

Solution steps

x \to 0 lim (\frac{x}{arcsin ( x )})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{1}{\frac{1}{1 - 0 ^{2}}}

Simplify

\frac{1}{\frac{1}{1 - 0 ^{2}}} : 1

= 1

x \to 7 + lim (\frac{1}{( x - 7 ) ^{2}} + 1)

x \to 1 lim (5 x)

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

x \to 0 lim (x + 2 - 1)

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

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