Question Number 73560 by mhmd last updated on 13/Nov/19 $${prove}\:{that}\:\left(\mathrm{1}−{itan}\theta\right)/\left({i}+{cot}\theta\right)={itan}\theta \\ $$$${pleas}\:{sir}\:{help}\:{me}? \\ $$ Commented by MJS last updated on 13/Nov/19 $$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{generally}\:\mathrm{true} \\ $$$$\frac{\mathrm{1}−\mathrm{i}\:\mathrm{tan}\:\theta}{\mathrm{i}+\mathrm{cot}\:\theta}=\mathrm{2sin}\:\theta\:\mathrm{cos}\:\theta\:−\mathrm{tan}\:\theta\:−\mathrm{2i}\:\mathrm{sin}^{\mathrm{2}} \:\theta…
Question Number 8025 by Nayon last updated on 28/Sep/16 $${find}\:{factor}\:{of}\:\gg \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{2}^{\mathrm{4}{n}+\mathrm{2}} +\mathrm{1}\right) \\ $$$${at}\:{the}\:{same}\:{way}\:{expand}\:\mathrm{2}^{\mathrm{58}} +\mathrm{1} \\ $$$$ \\ $$ Commented by Rasheed Soomro last…
Question Number 73561 by Rio Michael last updated on 13/Nov/19 $${find}\:{the}\:{value}\:{of}\:\lambda\:{for}\:{which} \\ $$$$\:{f}\::\:{x}\:\rightarrow\:\begin{cases}{\mathrm{2}\lambda\:−\:{x},\:{if}\:{x}\:<\:\mathrm{1}}\\{\lambda^{\mathrm{2}} \:+\:{x}\:−\mathrm{1},\:{if}\:{x}\:>\:\mathrm{1}}\end{cases} \\ $$$${has}\:{a}\:{limit}\:{as}\:{x}\rightarrow\:\mathrm{1} \\ $$ Answered by ajfour last updated on 13/Nov/19…
Question Number 139092 by mathdanisur last updated on 22/Apr/21 $$\Omega=\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{xsinh}\left(\pi{x}\right){e}^{−{x}^{\mathrm{2}} } }{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 8022 by Nayon last updated on 28/Sep/16 $$ \\ $$$${prove}\:{that}\:\forall{x}\in\boldsymbol{{N}}\: \\ $$$$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}\right)^{\mathrm{2}} \:\:{is}\:{a}\:{proper} \\ $$$${square}\:{number}. \\ $$ Commented by prakash jain…
Question Number 73555 by Rio Michael last updated on 13/Nov/19 $${find}\: \\ $$$$\left.{a}\right)\:\:\underset{{x}\rightarrow−\infty} {{Lim}}\:\frac{{ln}\left(\mathrm{1}+{e}^{{x}} \right)}{{e}^{{x}} } \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow+\infty} {{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{3}{x}}\:\:−{x}\right) \\ $$$$\left.{c}\right)\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\sqrt{{x}}\:{ln}\left({sinx}\right) \\ $$$$\left.{d}\right)\:\:\underset{{x}\rightarrow+\infty}…
Question Number 73552 by Rio Michael last updated on 13/Nov/19 $${evaluate}\: \\ $$$$\underset{{x}\rightarrow+\infty} {\:{Lim}}\:{xln}\:\left(\frac{{x}+\mathrm{1}}{{x}}\right) \\ $$ Commented by mathmax by abdo last updated on 13/Nov/19…
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Question Number 73553 by 01 last updated on 13/Nov/19 $$\mathrm{give}:\:\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{if}\:\mathrm{a}\mid\mathrm{b}\:\mathrm{and}\:\mathrm{b}\mid\mathrm{c} \\ $$$$\mathrm{prove}\::\:\mathrm{a}\mid\mathrm{c} \\ $$ Answered by Rio Michael last updated on 13/Nov/19 $${a}\mid{b}\:\Leftrightarrow\:\exists\:{k}\in\mathbb{Z}\::\:\:{b}\:=\:{ka}\:……\left({i}\right)…
Question Number 8016 by Nayon last updated on 28/Sep/16 $$ \\ $$$$ \\ $$$$\:{if}\:{x}\neq\mathrm{0}\:{then} \\ $$$${prove}\rightarrow \\ $$$$\:\:\:\:\frac{{x}^{\mathrm{4}} +{x}^{−\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{3}} +{x}^{−\mathrm{3}} }=\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}}−\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{1}} \\…