Question Number 131717 by LYKA last updated on 07/Feb/21 $${the}\:{temperature}\:{of}\:{a}\:{fluid} \\ $$$${in}\:{heating}\:{unit}\:{of}\:{a}\:{plant}\:{is}\:{given}\:{by} \\ $$$${T}\left({x}.{y}.{z}\right)=\:\frac{\mathrm{100}\left({z}−\mathrm{3}\right)}{\mathrm{10}−\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$${find}\:{the}\:{minimum}\:{and}\:{maximum}\: \\ $$$${temperatures}\:{if}\:{the}\:{heat}\:{exchanging}\: \\ $$$${components}\:{have}\:{the}\:{shapes}\: \\ $$$${z}=\frac{{x}^{\mathrm{2}} }{\mathrm{4}}−\frac{{y}^{\mathrm{2}}…
Question Number 647 by 123456 last updated on 18/Feb/15 $$\mathrm{log}_{{x}} \left({y}^{\pi} \right)+\mathrm{log}_{{y}} \left({x}^{{e}} \right)={a} \\ $$$$\frac{\mathrm{1}}{\mathrm{log}_{{y}} \left({x}^{\pi^{−\mathrm{1}} } \right)}−\frac{\mathrm{1}}{\mathrm{log}_{{x}} \left({y}^{{e}^{−\mathrm{1}} } \right)}={b} \\ $$$$\frac{{x}^{{a}+{b}+\mathrm{2}{e}} }{{y}^{{a}−{b}+\mathrm{2}\pi}…
Question Number 66183 by 0ister D1Id0 last updated on 10/Aug/19 $$\mathrm{why}\:\underset{{j}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({j}^{\mathrm{2}} {x}\right)}{{j}^{\mathrm{2}} }\:\mathrm{can}'\mathrm{t}\:\mathrm{differantial} \\ $$$$\mathrm{anywhere}??\:\:\mathrm{plz}\:\mathrm{ploof}….\mathrm{help} \\ $$ Commented by mathmax by abdo last…
Question Number 131718 by LYKA last updated on 07/Feb/21 $$\boldsymbol{{find}}\:\:\boldsymbol{{and}}\:\boldsymbol{{classify}}\:\boldsymbol{{the}}\:\boldsymbol{{stationary}} \\ $$$$\boldsymbol{{points}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)=\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} \left(\boldsymbol{{y}}−\mathrm{2}\right)\left(\boldsymbol{{x}}−\mathrm{2}\boldsymbol{{y}}\right)\left(\boldsymbol{{xy}}+\mathrm{4}\right) \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 131713 by mohammad17 last updated on 07/Feb/21 $${find}\:{all}\:{root}\:{by}\:{demover}\:{Z}^{\mathrm{4}} =\mathrm{2}−\mathrm{2}{i} \\ $$ Answered by mathmax by abdo last updated on 07/Feb/21 $$\mathrm{2}−\mathrm{2i}\:=\mathrm{2}\left(\mathrm{1}−\mathrm{i}\right)\:=\mathrm{2}\sqrt{\mathrm{2}}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{i}}{\:\sqrt{\mathrm{2}}}\right)=\mathrm{2}\sqrt{\mathrm{2}}\mathrm{e}^{−\frac{\mathrm{i}\pi}{\mathrm{4}}} \:=\mathrm{2}^{\frac{\mathrm{3}}{\mathrm{2}}} \:\mathrm{e}^{−\frac{\mathrm{i}\pi}{\mathrm{4}}}…
Question Number 131711 by mnjuly1970 last updated on 07/Feb/21 $$\:\:\:\:\:\:\:{advanced}\:\:{cslculus}\:.. \\ $$$$\:\:{prove}\:\:{that}: \\ $$$$\:\:\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{16}^{{n}} }\left(\frac{\mathrm{4}}{\mathrm{8}{n}+\mathrm{1}}−\frac{\mathrm{2}}{\mathrm{8}{n}+\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{8}{n}+\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{8}{n}+\mathrm{6}}\right)=\pi \\ $$ Commented by JDamian last updated on…
Question Number 66172 by mathmax by abdo last updated on 10/Aug/19 $$ \\ $$$${let}\:{A}_{{n}} =\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)\:\:\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\frac{{ln}\left({A}_{{n}} \right)}{{n}} \\ $$ Commented by…
Question Number 66173 by Tony Lin last updated on 10/Aug/19 $${x}^{{x}^{{x}\centerdot^{.^{.{x}} } } } =\mathrm{2} \\ $$$${x}=? \\ $$ Answered by mr W last updated…
Question Number 636 by 123456 last updated on 17/Feb/15 $${if}\:{f},{g}\:{are}\:{functions}\:{of}\:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${not}\:{constant}\:{such}\:{for}\:{all}\:\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} \\ $$$$\begin{cases}{{f}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)−{g}\left({x}\right){g}\left({y}\right)}\\{{g}\left({x}+{y}\right)={f}\left({x}\right){g}\left({y}\right)+{g}\left({x}\right){f}\left({y}\right)}\end{cases} \\ $$$${if}\:{f}'\left(\mathrm{0}\right)=\mathrm{0}\:{then}\:{proof}\:{os}\:{disproof} \\ $$$${that}\:\forall{x}\in\mathbb{R},\left[{f}\left({x}\right)\right]^{\mathrm{2}} +\left[{g}\left({x}\right)\right]^{\mathrm{2}} =\mathrm{1} \\ $$ Commented by prakash…
Question Number 66170 by mathmax by abdo last updated on 10/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{sin}\left({x}^{\mathrm{3}} \right){dx} \\ $$ Commented by mathmax by abdo last updated on…