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

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

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limit as x approaches 0 of cot(x)arcsin(x)

x \to 0 lim (cot (x) arcsin (x))

1

Solution steps

x \to 0 lim (cot (x) arcsin (x))

Rewrite for L'Hopital

= x \to 0 lim (\frac{arcsin ( x )}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= 1

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