LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES4 Marks
Question
Find $\lim\limits_{\text{x}\rightarrow5}\text{f}(\text{x})$, where $\text{f}(\text{x})=|\text{x}|-5$
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Answer
The given function is $\text{f}(\text{x})=|\text{x}|-5$. $=\lim\limits_{\text{x}\rightarrow5^-}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow5^-}\big[{|\text{x}|-5}\big]$ $=\lim\limits_{\text{x}\rightarrow5}\big({\text{x}-5}\big)$ [When x>0,$|\text{x}|=\text{x}$] $=5-5$$=0$
$\lim\limits_{\text{x}\rightarrow5^+}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow5^+}\big[{|\text{x}|-5}\big]$
$=\lim\limits_{\text{x}\rightarrow5}\big[{\text{x}-5}\big]$ [When x>0,$|\text{x}|=\text{x}$] $=5-5$ $=0$ $\therefore\lim\limits_{\text{x}\rightarrow5^-}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow5^+}\text{f}(\text{x})=0$ Hence,$\lim\limits_{\text{x}\rightarrow5}\text{f}(\text{x})=0$
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