What is the limit as x approaches 0 of (arcsin(x))/(7x) ?

The limit as x approaches 0 of (arcsin(x))/(7x) is 1/7

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limit as x approaches 0 of (arcsin(x))/(7x)

x \to 0 lim (\frac{arcsin ( x )}{7 x})

\frac{1}{7}

Decimal Notation

0.14285 \dots

Solution steps

x \to 0 lim (\frac{arcsin ( x )}{7 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{7} \cdot x \to 0 lim (\frac{arcsin ( x )}{x})

Apply L'Hopital's Rule

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

= \frac{1}{7} \cdot x \to 0 lim (\frac{\frac{1}{1 - x ^{2}}}{1})

Plug in the value

x = 0

= \frac{1}{7} \cdot \frac{\frac{1}{1 - 0 ^{2}}}{1}

Simplify

\frac{1}{7} \cdot \frac{\frac{1}{1 - 0 ^{2}}}{1} : \frac{1}{7}

= \frac{1}{7}

f (x) = sin^{4} (x), g (x) = sin^{2} (x)

t \to 0 lim (\frac{e ^{8 t} - 1}{t})

\int e^{x} 2 x d x

\frac{d}{d x} ((\frac{2}{x} + x^{5}) (x^{3} + 1))

\frac{\partial}{\partial p} (arctan (pq r))

What is the limit as x approaches 0 of (arcsin(x))/(7x) ?
The limit as x approaches 0 of (arcsin(x))/(7x) is 1/7