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 )})

= 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

\int \frac{1}{7 - 2 x} d x

\frac{d y}{d x} = \frac{( 2 y + 3 ) ^{2}}{( 4 x + 5 ) ^{2}}

\frac{d}{d x} (- \frac{2 x}{( - 4 + x ^{2} ) ^{2}})

\frac{\partial}{\partial x} (x^{a} y^{b} z^{c})

y = (\frac{1}{2 x + 1} - 2)^{3}

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