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

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

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limit as x approaches 0 of (sin(x))/(arcsin(x))

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{cos ( 0 )}{\frac{1}{1 - 0 ^{2}}}

Simplify

\frac{cos ( 0 )}{\frac{1}{1 - 0 ^{2}}} : 1

= 1

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

x \to - 1 lim (x^{2} - 5 x)

x \to 1 + lim (lo g_{x} (\frac{1}{3}))

x \to 3 + lim (\frac{1}{x})

x \to 0 lim (cos (x) - cot (x))

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