First slide

Introduction to limits

Question

$lim_{x \to \infty} \sqrt{\frac{x + \sin x}{x - \cos x}} =$

Moderate

Solution

We have,
$lim_{x \to \infty} \sqrt{\frac{x + \sin x}{x - \cos x}} = lim_{x \to \infty} \sqrt{\frac{1 + \frac{\sin x}{x}}{1 - \frac{\cos x}{x}}} = \sqrt{\frac{1 + 0}{1 - 0}} = 1$

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