Evaluate `lim_(xto0^(+)) (1)/(x)cos^(-1)((sinx)/(x))`.

Explanation

To evaluate the limit \( \lim_{x \to 0^+} \frac{1}{x} \cos^{-1}\left(\frac{\sin x}{x}\right) \), we can follow these steps:

### Step 1: Rewrite the limit
Since we are taking the limit as \( x \) approaches \( 0 \) from the right, we can denote \( x \) as \( h \) where \( h \to 0^+ \). Thus, we rewrite the limit as:
\[ \lim_{h \to 0^+} \frac{1}{h} \cos^{-1}\left(\frac{\sin h}{h}\right) \]

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