Trigonometry Homework: Solving lim (sin-1 x) / x with Given Equation

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Homework Statement




Solve limx->0 (sin-1 x) / x


Homework Equations



given limx->0 (sin x) / x = 1

The Attempt at a Solution

 
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Your post is vague; I have no idea what level of calculus you are working on or what attempts you have made to find the solution. L'Hospital's rule certainly applies though (form 0/0).
 
You can do without L'Ho^pital's rule. Make a subsitution x=sin p. What do you get ?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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