What is the limit as x approaches 1-of (arccos(x))/(sqrt(1-x^2)) ?

The limit as x approaches 1-of (arccos(x))/(sqrt(1-x^2)) is 1

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limit as x approaches 1-of (arccos(x))/(sqrt(1-x^2))

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Simplify

\frac{- \frac{1}{1 - x ^{2}}}{- \frac{x}{1 - x ^{2}}} : \frac{1}{x}

= x \to 1 - lim (\frac{1}{x})

Plug in the value

x = 1

= \frac{1}{1}

Simplify

= 1

x \to - 6 + lim (\frac{x}{x + 6})

x \to 2 lim (3 x^{2} + 4)

x \to 5 - lim (\frac{- 3}{x - 5})

x \to 1 lim (3 x - 2)

x \to 3 - lim (\frac{2 x}{9 - x ^{2}})

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