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Question
\[\lim_{x \to 0} \frac{x \cos x + \sin x}{x^2 + \tan x}\]
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Solution
\[\lim_{x \to 0} \left[ \frac{x \cos x + \sin x}{x^2 + \tan x} \right]\]
\[\text{ Dividing the numerator and the denominator by } x:\]
\[ \lim_{x \to 0} \left[ \frac{\cos x + \frac{\sin x}{x}}{x + \frac{\tan x}{x}} \right]\]
\[ = \frac{\cos 0 + 1}{0 + 1}\]
\[ = 2\]
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