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Limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits3 Marks
Question
Find $\lim\limits_{\text{x}\rightarrow3}\text{f(x)},$ where $\text{f(x)}=\begin{cases}4, & \text{if x}> 3\\\text{x}+1, &\text{if x} < 3\end{cases}.$
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Answer

$\lim\limits_{\text{x}\rightarrow3^+}\text{f(x)}=4$
$\lim\limits_{\text{x}\rightarrow3^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow3^-}\text{(x}+1)=\lim\limits_{\text{h}\rightarrow0}(3-\text{h}+1)=3+1=4$
Since, $\lim\limits_{\text{x}\rightarrow3^+}\text{f(x)}=4=\lim\limits_{\text{x}\rightarrow3^-}\text{f(x)}$
$\therefore\ \lim\limits_{\text{x}\rightarrow3}\text{f(x) is }4$

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