Question Number 167699 by HongKing last updated on 23/Mar/22 Answered by alephzero last updated on 23/Mar/22 $$\mathrm{1}.\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}}{{x}\:\mathrm{sin}\:{x}}\:\overset{\mathrm{use}\:\mathrm{L}'\mathrm{H}\hat {\mathrm{o}pital}'\mathrm{s}\:\mathrm{rule}} {=} \\ $$$$=\:\mathrm{lim}\:\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}+{x}\:\mathrm{cos}\:{x}}\:\overset{\mathrm{again}} {=} \\ $$$$=\:\mathrm{lim}\:\frac{\mathrm{cos}\:{x}}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:=…
Question Number 167690 by peter frank last updated on 22/Mar/22 Answered by som(math1967) last updated on 23/Mar/22 $${by}\:{solving}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4}\:{and}\:\left({x}−\mathrm{2}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4} \\ $$$${x}=\mathrm{1}\:,{y}=\pm\sqrt{\mathrm{3}} \\…
Question Number 167664 by Ari last updated on 22/Mar/22 $${a}=\mathrm{3}{k},{b}=\mathrm{4}{k},{c}=\mathrm{5}{k} \\ $$$$\mathrm{3}{k}+\mathrm{4}{k}+\mathrm{5}{k}=\mathrm{1000}\Rightarrow{k}=\mathrm{500}/\mathrm{6} \\ $$$${a}=\mathrm{1500}/\mathrm{6},{b}=\mathrm{200}/\mathrm{6},{c}=\mathrm{2500}/\mathrm{6} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167648 by mathlove last updated on 22/Mar/22 $$\mathrm{log}_{{sinx}} \mathrm{2}+\mathrm{log}_{{cosx}} \mathrm{2}+{log}_{\mathrm{sin}\:{x}} \mathrm{2}×{log}_{\mathrm{cos}\:{x}} \mathrm{2}=\mathrm{0} \\ $$$${x}=? \\ $$ Commented by Rasheed.Sindhi last updated on 22/Mar/22…
Question Number 102109 by Jamshidbek2311 last updated on 06/Jul/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167627 by HongKing last updated on 21/Mar/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 102078 by Jamshidbek2311 last updated on 06/Jul/20 Answered by mr W last updated on 06/Jul/20 $$\boldsymbol{{METHOD}}\:\boldsymbol{{I}} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{is}\:{the}\:{square}\:{of}\:{the}\:{distance} \\ $$$${from}\:{point}\:\left({x},{y}\right)\:{to}\:{the}\:{origin}\:\left(\mathrm{0},\mathrm{0}\right). \\…
Question Number 167612 by infinityaction last updated on 20/Mar/22 Commented by Rasheed.Sindhi last updated on 21/Mar/22 $$\mathcal{D}{etermine}\:{all}\:{the}\:{possible}\:{triples} \\ $$$$\left({a},{b},{c}\right)\:{of}\:{positive}\:{integers}\:{for}\:{which} \\ $$$${ab}−{c},{bc}−{a}\:{and}\:{ca}−{b}\:{are}\:{powers}\:{of} \\ $$$$\mathrm{2}. \\ $$…
Question Number 167601 by HongKing last updated on 20/Mar/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167566 by infinityaction last updated on 19/Mar/22 Answered by MJS_new last updated on 19/Mar/22 $${x}={u}−{v}\wedge{y}={u}+{v} \\ $$$${z}=\mathrm{1}−\mathrm{2}{u} \\ $$$${z}^{\mathrm{2}} =\mathrm{1}−\mathrm{2}\left({u}^{\mathrm{2}} +{v}^{\mathrm{2}} \right) \\…