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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\cos\text{x}+\sin\text{x}}{\text{x}^2+\tan\text{x}}$
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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\cos\text{x}+\sin\text{x}}{\text{x}^2+\tan\text{x}}$ $=\lim\limits_{\text{x} \rightarrow0}\frac{\cos\text{x}+\frac{\sin\text{x}}{\text{x}}}{\text{x}+\frac{\tan\text{x}}{\text{x}}}$ $=\frac{\lim\limits_{\text{x} \rightarrow0}\cos\text{x}+\lim\limits_{\text{x} \rightarrow0}\frac{\sin\text{x}}{\text{x}}}{\lim\limits_{\text{x} \rightarrow0}\text{x}+\lim\limits_{\text{x} \rightarrow0}\frac{\tan\text{x}}{\text{x}}}$ $=\frac{1+1}{0+1}=\frac21$ $=2$

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