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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
Question
Fill in the blanks.
If $\text{f}(\text{x})=\frac{\tan\text{x}}{\text{x}-\pi}$ then $\lim\limits_{\text{x} \rightarrow \pi}\text{f}(\text{x})=$ ____________.
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Answer

If $\text{f}(\text{x})=\frac{\tan\text{x}}{\text{x}-\pi}$ then $\lim\limits_{\text{x} \rightarrow \pi}\text{f}(\text{x})=\lim\limits_{\pi \rightarrow 0}\frac{-\tan(\pi-\text{x})}{-(\pi-\text{x})}$Solution:
Given $\text{f}(\text{x})=\lim\limits_{\text{x} \rightarrow \pi}\text{f}(\text{x})=\lim\limits_{\pi \rightarrow 0}\frac{-\tan(\pi-\text{x})}{-(\pi-\text{x})}$ $=1$ Hence, the value of the filler is 1.

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