Question Number 145851 by mathdanisur last updated on 08/Jul/21 $${if}\:\:\underset{{x}\rightarrow\infty} {{lim}}\frac{\left({a}-\mathrm{3}\right){x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +{cx}+\mathrm{4}}{{bx}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{7}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${find}\:\:{a}+{b}=? \\ $$ Answered by Olaf_Thorendsen last updated on 08/Jul/21…
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Question Number 80306 by Power last updated on 02/Feb/20 Commented by mr W last updated on 02/Feb/20 $${use}\:{your}\:{calculator}\:{and}\:{you}\:{will}\:{get} \\ $$$${something}\:{like}\:\mathrm{0}.\mathrm{71828}….\:{which}\:{is} \\ $$$${nearly}\:{equal}\:{to}\:{e}−\mathrm{2},\:{but}\:{only}\:{nearly}. \\ $$ Terms…
Question Number 14775 by tawa tawa last updated on 04/Jun/17 $$\mathrm{Using}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{factorize}\:\mathrm{completely}\:\mathrm{the}\:\mathrm{expression}\: \\ $$$$\mathrm{x}^{\mathrm{3}} \left(\mathrm{y}\:−\:\mathrm{z}\right)\:+\:\mathrm{y}^{\mathrm{3}} \left(\mathrm{z}\:−\:\mathrm{x}\right)\:+\:\mathrm{z}^{\mathrm{3}} \left(\mathrm{x}\:−\:\mathrm{y}\right)\: \\ $$ Answered by ajfour last updated on 04/Jun/17…
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Question Number 145835 by mathdanisur last updated on 08/Jul/21 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {{lim}}\left({sin}\mathrm{2}{x}\centerdot{tgx}\right)=? \\ $$ Answered by bramlexs22 last updated on 09/Jul/21 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}.\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}}\:=\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}2sin}\:^{\mathrm{2}} \mathrm{x} \\…
Question Number 14747 by 433 last updated on 04/Jun/17 $$\epsilon>\mathrm{0} \\ $$$$\mathrm{6}−\epsilon\leqslant{xy}\leqslant\mathrm{6}+\epsilon \\ $$$$\mathrm{5}−\epsilon\leqslant{x}+{y}\leqslant\mathrm{5}+\epsilon \\ $$$${Find}\:{x}\:\&\:{y} \\ $$ Answered by ajfour last updated on 04/Jun/17…
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Question Number 145801 by mathdanisur last updated on 08/Jul/21 Answered by ajfour last updated on 08/Jul/21 $${xy}+{tz}={a} \\ $$$${solving}\:{for}\:{x},{y}\:{in}\:{terms}\:{of} \\ $$$${t},{z}\:{from}\:\mathrm{2}{nd}\:{and}\:\mathrm{3}{rd}\:{eqs}. \\ $$$${x}=\frac{{bz}−{ct}}{{z}^{\mathrm{2}} −{t}^{\mathrm{2}} }\:\:;\:\:{y}=\frac{{bt}−{cz}}{{t}^{\mathrm{2}}…