Question Number 5130 by Apoorva last updated on 16/Apr/16 $$\mathrm{2}\:{to}\:{the}\:{power}\:{x}+\mathrm{2}\:{to}\:{the}\:{power}\:\left(−{x}+\mathrm{1}\right)−\mathrm{3}<\mathrm{0}.{ease}\:{ans}\:{asap} \\ $$ Commented by prakash jain last updated on 17/Apr/16 $$\mathrm{2}^{\left({x}+\mathrm{2}\right)^{\left(−{x}+\mathrm{1}\right)−\mathrm{3}} } <\mathrm{0} \\ $$$$\mathrm{If}\:{x}\in\mathbb{R}\:\mathrm{then}\:\mathrm{2}^{\left({x}+\mathrm{2}\right)^{\left(−{x}+\mathrm{1}\right)−\mathrm{3}}…
Question Number 136197 by Ar Brandon last updated on 19/Mar/21 $$\mathrm{a}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{real}\:\mathrm{constant}\:\mathrm{a}\:\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\frac{\mathrm{a}}{\mathrm{x}^{\mathrm{2}} }} \mathrm{dx}=\infty \\ $$$$\mathrm{b}.\:\mathrm{If}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\mathrm{real}\:\mathrm{constants},\:\mathrm{explain}\:\mathrm{why}\:\mathrm{we}\:\mathrm{cannot}\:\mathrm{split}\:\mathrm{the} \\ $$$$\mathrm{integral}\:\:\int_{\mathrm{0}} ^{\infty} \left(\mathrm{e}^{−\frac{\mathrm{a}}{\mathrm{x}^{\mathrm{2}} }} −\mathrm{e}^{−\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{2}} }} \right)\mathrm{dx}\:\mathrm{as}\:\mathrm{the}\:\mathrm{difference}\:\int_{\mathrm{0}}…
Question Number 5125 by Rojaye Shegz last updated on 16/Apr/16 Commented by Rojaye Shegz last updated on 16/Apr/16 $$\mathrm{Sorry},\:\mathrm{that}\:\mathrm{was}\:\mathrm{an}\:\mathrm{error}. \\ $$$$\frac{\mathrm{p}}{\mathrm{q}}\:\mathrm{is}\:\mathrm{the}\:\left\{\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{p}+\mathrm{q}−\mathrm{1}\right)\left(\mathrm{p}+\mathrm{q}−\mathrm{2}\right)+\mathrm{p}\right\}\mathrm{th}\:\mathrm{term} \\ $$ Commented by…
Question Number 70659 by aliesam last updated on 06/Oct/19 $${find}\:{the}\:{range}\:{algrbraically} \\ $$$$ \\ $$$${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} −\mathrm{1}} \\ $$ Answered by MJS last updated on 06/Oct/19 $$\sqrt{{x}^{\mathrm{2}}…
Question Number 5122 by FilupSmith last updated on 16/Apr/16 $$\mathrm{Lets}\:\mathrm{say}\:\mathrm{person}\:\mathrm{1}\:\mathrm{punches}\:\mathrm{a}\:\mathrm{bag}\:\mathrm{and}\: \\ $$$$\mathrm{the}\:\mathrm{punch}\:\mathrm{is}\:\mathrm{fast}\:\mathrm{from}\:\mathrm{start}\:\mathrm{to}\:\mathrm{finish}. \\ $$$$ \\ $$$$\mathrm{Lets}\:\mathrm{say}\:\mathrm{person}\:\mathrm{2}\:\mathrm{does}\:\mathrm{a}\:\mathrm{punch}\:\mathrm{but} \\ $$$$\mathrm{only}\:\mathrm{the}\:\mathrm{final}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{punch}\:\mathrm{is}\:\mathrm{fast}. \\ $$$$ \\ $$$$\mathrm{How}\:\mathrm{will}\:\mathrm{the}\:\mathrm{forces}\:\mathrm{differ}\:\mathrm{in}\:\mathrm{these}\:\mathrm{punches}? \\ $$$$ \\…
Question Number 5121 by Yozzii last updated on 15/Apr/16 $${What}\:{solutions}\:{x}\in\mathbb{R}\:{exist}\:{for}\:{the}\: \\ $$$${equation}\:\left({tan}^{−\mathrm{1}} {x}\right)\left({cot}^{−\mathrm{1}} {x}\right)={n} \\ $$$${where}\:{n}\in\mathbb{Z}? \\ $$ Answered by prakash jain last updated on…
Question Number 5119 by sanusihammed last updated on 14/Apr/16 Commented by 123456 last updated on 15/Apr/16 $${x}=\sqrt{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}} \\ $$$${x}^{\mathrm{2}} =\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}} \\ $$$${x}=\sqrt{{a}}+\sqrt{{b}}\wedge{a}>\mathrm{0}\wedge{b}>\mathrm{0} \\ $$$${x}^{\mathrm{2}} ={a}+{b}+\mathrm{2}\sqrt{{ab}}…
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Question Number 5117 by FilupSmith last updated on 14/Apr/16 $$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{question}.\:\mathrm{I}\:\mathrm{am}\:\mathrm{unsure}\:\mathrm{how}\:\mathrm{this} \\ $$$$\mathrm{is}\:\mathrm{done}\:\mathrm{because}\:\mathrm{I}\:\mathrm{have}\:\mathrm{never}\:\mathrm{learnt}\:\mathrm{it}. \\ $$$$ \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{line}\:\mathrm{of}\:\mathrm{best}\:\mathrm{fit}? \\ $$ Commented by Yozzii last updated on 14/Apr/16…
Question Number 70653 by naka3546 last updated on 06/Oct/19 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\:\left(\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\right)^{\mathrm{tan}\:{x}} \:\:=\:\:… \\ $$ Commented by kaivan.ahmadi last updated on 06/Oct/19 $${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \left({sinx}−{cosx}−\mathrm{1}\right){tanx}= \\ $$$${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}}…