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Derivative of Standard Inverse Trigonometric Functions

Evaluate: li...

Question

Evaluate:
$lim x \to 0 \frac{| cos (sin 3 x) | - 1}{x^{2}}$

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Solution

$lim x \to 0 \frac{| cos (sin 3 x) | - 1}{x^{2}} = lim x \to 0 \frac{cos (sin 3 x) - 1}{x^{2}} = lim x \to 0 \frac{- 3 sin (sin 3 x) cos 3 x}{2 x} = - \frac{9}{2}$

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