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Question Number 183353 by Spillover last updated on 25/Dec/22
For the function  f(x)= { ((x^2 −3 if x<4)),(((x^2 /(x+4))     if x≥4)) :}  Find (i) lim_(x→−4)  f(x)      ii)lim_(x→+4)  f(x)
$${For}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3}\:{if}\:{x}<\mathrm{4}}\\{\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{4}}\:\:\:\:\:{if}\:{x}\geqslant\mathrm{4}}\end{cases} \\ $$$$\left.{Find}\:\left({i}\right)\:\underset{{x}\rightarrow−\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right)\:\:\:\:\:\:{ii}\right)\underset{{x}\rightarrow+\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right) \\ $$
Answered by TheSupreme last updated on 25/Dec/22
i) lim=f(−4)=13  ii) lim→4^− =13    lim → 4^+  = 2
$$\left.{i}\right)\:{lim}={f}\left(−\mathrm{4}\right)=\mathrm{13} \\ $$$$\left.{ii}\right)\:{lim}\rightarrow\mathrm{4}^{−} =\mathrm{13} \\ $$$$\:\:{lim}\:\rightarrow\:\mathrm{4}^{+} \:=\:\mathrm{2} \\ $$$$ \\ $$

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