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Lim X → 0 X Cos X + Sin X X 2 + Tan X - Mathematics

\[\lim_{x \to 0} \frac{x \cos x + \sin x}{x^2 + \tan x}\] 

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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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.7 | Q 46 | Page 51
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