Question Number 118798 by WasimShaikh last updated on 19/Oct/20 $$\left.\:\mathrm{1}\right){Find}\:\frac{{dy}}{{dx}}\:\:;\:\:\:{if}\:\:\:{x}\:=\:{at}^{\mathrm{2}} \:,\:\:{y}\:=\:\mathrm{2}{at} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\: \\ $$ Answered by Dwaipayan Shikari last updated on 20/Oct/20…
Question Number 118791 by Algoritm last updated on 19/Oct/20 Answered by Olaf last updated on 19/Oct/20 $${f}_{{p}} \left({a}\right)\:=\:\underset{{n}=\mathrm{1}} {\overset{{p}} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}{n}\ast{a}\right)}{\mathrm{2}^{{n}} } \\ $$$${f}_{{p}} \left({a}\right)\:=\:\underset{{n}=\mathrm{1}} {\overset{{p}}…
Question Number 118776 by obaidullah last updated on 19/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{sinx}}{{x}^{\mathrm{3}} }=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{x}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}}{{x}^{\mathrm{3}} } \\ $$$$\Rightarrow\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{3}!}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$ Terms of Service Privacy Policy…
Question Number 118781 by Algoritm last updated on 19/Oct/20 Commented by MJS_new last updated on 19/Oct/20 $$\mathrm{minimum}\:\mathrm{of}\:{f}\left({x}\right)={x}^{{x}^{{x}^{{x}} } } \:\mathrm{is}\:\approx.\mathrm{59} \\ $$$$\mathrm{but}\:\frac{\mathrm{1}}{\mathrm{3}^{\sqrt{\mathrm{48}}} }\approx.\mathrm{00049} \\ $$$$\Rightarrow\:\mathrm{no}\:\mathrm{solution}…
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Question Number 118768 by mathdave last updated on 19/Oct/20 Answered by mindispower last updated on 23/Oct/20 $$\underset{{m}=\mathrm{0}} {\overset{{n}} {\sum}}{e}^{{imx}} =\frac{\mathrm{1}−\left({e}^{{ix}} \right)^{{n}+\mathrm{1}} }{\mathrm{1}−{e}^{{ix}} }=\frac{{e}^{{i}\frac{{nx}}{\mathrm{2}}} \left({e}^{−{i}\frac{\left({n}+\mathrm{1}\right){x}}{\mathrm{2}}} −{e}^{{i}\frac{\left({n}+\mathrm{1}\right){x}}{\mathrm{2}}}…
Question Number 118757 by mohammad17 last updated on 19/Oct/20 Commented by mohammad17 last updated on 19/Oct/20 $${with}\:{out}\:{x}={tan}\:\theta \\ $$ Answered by mnjuly1970 last updated on…
Question Number 118759 by ZiYangLee last updated on 19/Oct/20 $$\mathrm{The}\:\mathrm{first}\:\mathrm{three}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{binomial}\:\mathrm{expansion} \\ $$$$\left({p}−{q}\right)^{{m}} \:,\:\mathrm{in}\:\mathrm{ascending}\:\mathrm{order}\:\mathrm{of}\:{q},\:\mathrm{are}\:\mathrm{denoted} \\ $$$$\mathrm{by}\:{a},{b}\:\mathrm{and}\:{c}\:\mathrm{respectively}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\frac{{b}^{\mathrm{2}} }{{ac}}=\frac{\mathrm{2}{m}}{{m}−\mathrm{1}} \\ $$ Commented by PRITHWISH SEN 2…
Question Number 53205 by mondodotto@gmail.com last updated on 19/Jan/19 Commented by MJS last updated on 22/Jan/19 $$\mathrm{2}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution} \\ $$$${t}_{\mathrm{1}} \left({x}\right)=\frac{\mathrm{25}^{{x}} }{\mathrm{5}^{{x}} }=\left(\frac{\mathrm{25}}{\mathrm{5}}\right)^{{x}} =\mathrm{5}^{{x}} ;\:{t}_{\mathrm{1}} \left(\mathrm{2}\right)=\mathrm{25}…
Question Number 118733 by mohammad17 last updated on 19/Oct/20 Commented by bemath last updated on 19/Oct/20 $$\left(\mathrm{4}\right)\:\frac{{d}}{{dx}}\:\left[\:\int\:_{{x}^{\mathrm{3}} } ^{\mathrm{2}{x}^{\mathrm{2}} } \:\mathrm{cos}\:\left(\mathrm{2}{t}^{\mathrm{3}} +\mathrm{1}\right)\:{dt}\:\right]\:= \\ $$$$\mathrm{4}{x}\:\mathrm{cos}\:\left(\mathrm{2}.\left(\mathrm{8}{x}^{\mathrm{6}} \right)+\mathrm{1}\right)−\mathrm{3}{x}^{\mathrm{2}}…