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Popular >

limit as x approaches 1/3 of (arcsin(x)-arcsin(1/3))/(x-1/3)

Solution

x \to \frac{1}{3} lim (\frac{arcsin ( x ) - arcsin ( \frac{1}{3} )}{x - \frac{1}{3}})

Solution

\frac{3}{2 2}

+1

Decimal

1.06066 \dots

Solution steps

x \to \frac{1}{3} lim (\frac{arcsin ( x ) - arcsin ( \frac{1}{3} )}{x - \frac{1}{3}})

Apply L'Hopital's Rule

: x \to \frac{1}{3} lim (\frac{\frac{1}{- x ^{2} + 1}}{1})

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

Plug in the value

x = \frac{1}{3}

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

Simplify

\frac{\frac{1}{- ( \frac{1}{3} ) ^{2} + 1}}{1} : \frac{3}{2 2}

= \frac{3}{2 2}

Graph

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Frequently Asked Questions (FAQ)

What is the limit as x approaches 1/3 of (arcsin(x)-arcsin(1/3))/(x-1/3) ?
The limit as x approaches 1/3 of (arcsin(x)-arcsin(1/3))/(x-1/3) is 3/(2sqrt(2))