Question Number 40667 by Tawa1 last updated on 25/Jul/18
![find the value lim_(x→0) g(x) must have, if g complies the statement about limit. Suppose lim_(x→ −4) [x lim_(x→0) g(x)] = 2](https://www.tinkutara.com/question/Q40667.png)
$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{x}\right)\:\:\mathrm{must}\:\mathrm{have},\:\mathrm{if}\:\mathrm{g}\:\mathrm{complies}\:\mathrm{the}\:\mathrm{statement}\: \\ $$$$\mathrm{about}\:\mathrm{limit}.\:\mathrm{Suppose}\:\:\:\underset{{x}\rightarrow\:−\mathrm{4}} {\mathrm{lim}}\:\:\left[\mathrm{x}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\mathrm{g}\left(\mathrm{x}\right)\right]\:\:=\:\:\mathrm{2} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jul/18
$${mobile}\:{handset}\:{does}\:{not}\:{show}\:{a}\:{few}\: \\ $$$${portion}\:{of}\:{problem}\:…{so}\:{pls}\:{check}\:…{repost}\:{the} \\ $$$${problem}\:{or}\:\:{check}\:{my}\:{answer}… \\ $$
Commented by Joel578 last updated on 26/Jul/18
$${have}\:{u}\:{tried}\:{to}\:{scroll}\:{sideways}? \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jul/18
![let lim_(x→0) g(x) =A where A is independent of x lim_(x→−4) [xlim_(x→0) g(x)] =2 given lim_(x→−4) A.x= 2 so −4A=2 A=((−1)/2) hence lim_(x→0) g(x)=((−1)/2) pls check...](https://www.tinkutara.com/question/Q40670.png)
$${let}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{g}\left({x}\right)\:={A} \\ $$$${where}\:{A}\:{is}\:{independent}\:{of}\:{x} \\ $$$$\underset{{x}\rightarrow−\mathrm{4}} {\mathrm{lim}}\:\left[{x}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{g}\left({x}\right)\right]\:=\mathrm{2}\:\:{given} \\ $$$$\underset{{x}\rightarrow−\mathrm{4}} {\mathrm{lim}}\:{A}.{x}=\:\:\mathrm{2} \\ $$$${so}\:−\mathrm{4}{A}=\mathrm{2} \\ $$$${A}=\frac{−\mathrm{1}}{\mathrm{2}}\:\:\:{hence}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{g}\left({x}\right)=\frac{−\mathrm{1}}{\mathrm{2}}\:\:\:{pls}\:{check}… \\ $$
Commented by Tawa1 last updated on 26/Jul/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jul/18
$${thank}\:{you},{that}\:{means}\:{i}\:{have}\:{reached}\:{the}\:_{} \\ $$$${destination}… \\ $$$$ \\ $$