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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits3 Marks
Question
If $\text{f(x)}=\begin{cases}2\text{x}+3, & \text{x} \le0\\3(\text{x}+1), &\text{x} > 0\end{cases}$Find $\lim\limits_{\text{x}\rightarrow0}\text{f(x)}$ and $\lim\limits_{\text{x}\rightarrow1}\text{f(x)}.$
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Answer

$\lim\limits_{\text{x}\rightarrow0^+}\text{f(x)}=\lim\limits_{\text{x}\rightarrow0^+}3\text{(x}+1)=3$ And, $\lim\limits_{\text{x}\rightarrow0^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow0^-}2\text{(x)}+3=3$ $\therefore\ \lim\limits_{\text{x}\rightarrow0}\text{f(x)}=3$ $\lim\limits_{\text{x}\rightarrow1}\text{f(x)}=\lim\limits_{\text{x}\rightarrow1}3(\text{x}+1)=3+3=6$ $\therefore\ \lim\limits_{\text{x}\rightarrow1}\text{f(x)}=6$

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