Question Number 125790 by mohammad17 last updated on 13/Dec/20 Answered by liberty last updated on 13/Dec/20 $$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\left({x}+\mathrm{2}\right)\left({x}−\mathrm{2}\right)}{\mathrm{sin}\:\pi{x}}\:=\:\mathrm{4}×\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\left[\:\frac{{x}−\mathrm{2}}{\mathrm{sin}\:\pi{x}}\:\right] \\ $$$$\:\left[\:{let}\:{x}=\mathrm{2}+{t}\:\wedge\:{t}\rightarrow\mathrm{0}\:\right]\: \\ $$$$=\:\mathrm{4}×\:\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{t}}{\mathrm{sin}\:\pi\left({t}+\mathrm{2}\right)}\:=\:\mathrm{4}\:×\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{t}}{\mathrm{sin}\:\left(\mathrm{2}\pi+\pi{t}\right)}…
Question Number 60240 by ANTARES VY last updated on 19/May/19 $$\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)}{\:\sqrt{\mathrm{4}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dx}} \\ $$ Commented by maxmathsup by imad last updated on 19/May/19…
Question Number 125758 by ZiYangLee last updated on 13/Dec/20 $$\Delta\mathrm{ABC}\:\mathrm{have}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10}\:\mathrm{13}\:\mathrm{13} \\ $$$$\mathrm{while}\:\Delta\mathrm{PQR}\:\mathrm{have}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{length} \\ $$$$\mathrm{13}\:\mathrm{13}\:\mathrm{24}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{Area}\:\mathrm{of}\:\Delta\mathrm{ABC}\::\:\mathrm{Area} \\ $$$$\mathrm{of}\:\Delta\mathrm{PQR}. \\ $$ Answered by mr W last…
Question Number 125739 by ZiYangLee last updated on 13/Dec/20 $$\mathrm{Given}\:\mathrm{that}\:{x}^{{x}^{\mathrm{4}} } =\mathrm{4},\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}^{{x}^{\mathrm{2}} } +{x}^{{x}^{\mathrm{8}} } . \\ $$ Commented by Dwaipayan Shikari last…
Question Number 191254 by anr0h3 last updated on 21/Apr/23 $$ \\ $$$${a}=\frac{{x}−{a}}{{x}−{b}}\:{solve}\:{for}\:{x} \\ $$$$\mathrm{did}\:\mathrm{i}\:\mathrm{make}\:\mathrm{anything}\:\mathrm{wrong}\:\mathrm{in}\:\mathrm{the}\:\mathrm{following}? \\ $$$$ \\ $$$$\mathrm{starpoint}: \\ $$$${ln}\mid{a}\mid={ln}\mid\frac{{x}−{a}}{{x}−{b}}\mid \\ $$$${ln}\mid{a}\mid={ln}\mid{x}−{a}\mid−{ln}\mid{x}−{b}\mid \\ $$$${ln}\mid{a}\mid={ln}\mid\frac{{x}}{{a}}\mid−{ln}\mid\frac{{x}}{{b}}\mid \\…
Question Number 191243 by sonukgindia last updated on 21/Apr/23 Commented by mr W last updated on 21/Apr/23 $${at}\:{x}=\mathrm{1}\:? \\ $$ Answered by PandaMa last updated…
Question Number 125697 by aurpeyz last updated on 13/Dec/20 $${what}\:{is}\:{the}\:{largest}\:{coefficient}\:{of}\: \\ $$$$\left(\mathrm{4}+\mathrm{3}{x}\right)^{−\mathrm{5}} ? \\ $$ Answered by mr W last updated on 13/Dec/20 $$\left(\mathrm{4}+\mathrm{3}{x}\right)^{−\mathrm{5}} \\…
Question Number 60152 by Kunal12588 last updated on 18/May/19 $${Join}\:{Telegram}\:{group} \\ $$$$@{booksforjee} \\ $$$${To}\:{get}\:{evry}\:{books}\:{pdfs} \\ $$$${related}\:{to}\:{NEET},\:{JEE}\left({MAIN}\:{ADVANCED}\right) \\ $$$${and}\:{all}\:{engineering}\:{entrance}\:{exam}\:{books} \\ $$$${Also} \\ $$$${Books}\:{for}\:{class}\:{XII},{XI},{X},{IX} \\ $$ Commented…
Question Number 191220 by anr0h3 last updated on 21/Apr/23 $${x}^{\mathrm{6}} −{x}^{\mathrm{3}} =\mathrm{2}\:{solve}\:{for}\:{x} \\ $$$$ \\ $$$${m}={x}^{\mathrm{3}} \\ $$$${m}^{\mathrm{2}} =\left({x}^{\mathrm{3}} \right)^{\mathrm{2}} \\ $$$${m}^{\mathrm{2}} −{m}=\mathrm{2} \\ $$$${m}^{\mathrm{2}}…
Question Number 125685 by Hassen_Timol last updated on 12/Dec/20 $$ \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$ \\ $$$$\:\:\:\:\:{q}_{\left({t}\right)} ''\:\:+\:\:\frac{\mathrm{1}}{\mathrm{LC}}\:{q}_{\left({t}\right)} \:\:=\:\:\frac{{V}}{{L}} \\ $$$$ \\ $$$$\mathrm{with}\:\left(\mathrm{L},\mathrm{C},\mathrm{V}\right)\:\in\:\mathbb{R}^{\mathrm{3}} \\ $$$$ \\…