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Author: Tinku Tara

Question-201184

Question Number 201184 by Calculusboy last updated on 01/Dec/23 Answered by Sutrisno last updated on 01/Dec/23 $${misal}\::\:\:\sqrt{\mathrm{2}{x}}+\mathrm{4}={u}\rightarrow{dx}=\sqrt{\mathrm{2}{x}}{du} \\ $$$$=\int\frac{\sqrt{\mathrm{2}{x}}}{{u}}.\sqrt{\mathrm{2}{x}}{du} \\ $$$$=\int\frac{\left({u}−\mathrm{4}\right)^{\mathrm{2}} }{{u}}{du} \\ $$$$=\int\frac{{u}^{\mathrm{2}} −\mathrm{8}{u}+\mathrm{16}}{{u}}{du}…

Question-201149

Question Number 201149 by Mingma last updated on 30/Nov/23 Answered by witcher3 last updated on 03/Dec/23 $$\mathrm{x}=\mathrm{n}\in\mathbb{N}\:\mathrm{y}=\frac{\mathrm{1}}{\mathrm{n}},\mathrm{z}=\frac{\mathrm{1}}{\mathrm{n}},\mathrm{n}\geqslant\mathrm{2} \\ $$$$\forall\mathrm{n}\in\mathbb{N}−\left\{\mathrm{0},\mathrm{1}\right\}\:\:\left(\mathrm{n},\frac{\mathrm{1}}{\mathrm{n}},\frac{\mathrm{1}}{\mathrm{n}}\right)\mathrm{is}\:\mathrm{solution} \\ $$$$ \\ $$ Terms of…

Question-201150

Question Number 201150 by Mingma last updated on 30/Nov/23 Answered by mr W last updated on 02/Dec/23 $${a}={side}\:{length}\:{of}\:{square} \\ $$$$\left(\frac{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{15}^{\mathrm{2}} }{\mathrm{2}{ax}}\right)^{\mathrm{2}} +\left(\frac{{a}^{\mathrm{2}} +{x}^{\mathrm{2}}…

14-15-6-45-28-6-

Question Number 201144 by sts313 last updated on 30/Nov/23 $$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{45}}{\mathrm{28}}\right)^{\mathrm{6}} = \\ $$ Answered by mathlove last updated on 01/Dec/23 $$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{3}×\mathrm{15}}{\mathrm{2}×\mathrm{14}}\right)^{\mathrm{6}} =\frac{\cancel{\mathrm{14}^{\mathrm{6}} }}{\cancel{\mathrm{15}^{\mathrm{6}}…

If-R-x-2-yi-2y-2-zj-xy-2-z-2-k-find-d-2-R-dx-2-d-2-R-dy-2-at-the-point-2-1-2-

Question Number 201140 by Calculusboy last updated on 30/Nov/23 $$\boldsymbol{{If}}\:\underset{−} {\boldsymbol{{R}}}=\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}\underset{−} {\boldsymbol{{i}}}−\mathrm{2}\boldsymbol{{y}}^{\mathrm{2}} \boldsymbol{{z}}\underset{−} {\boldsymbol{{j}}}+\boldsymbol{{xy}}^{\mathrm{2}} \boldsymbol{{z}}^{\mathrm{2}} \underset{−} {\boldsymbol{{k}}},\:\boldsymbol{{find}}\:\mid\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dx}}^{\mathrm{2}} }×\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dy}}^{\mathrm{2}} }\mid\:\: \\ $$$$\boldsymbol{{at}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\left(\mathrm{2},\mathrm{1},−\mathrm{2}\right) \\…

Question-201139

Question Number 201139 by cherokeesay last updated on 30/Nov/23 Commented by Frix last updated on 30/Nov/23 $${x}\approx\mathrm{6395}.\mathrm{12283}\wedge{y}\approx\mathrm{171}.\mathrm{458282} \\ $$$$\mathrm{Exact}\:\mathrm{solution}: \\ $$$${x}=\mathrm{32}\left(\mathrm{8}\left(\mathrm{5}{r}^{\mathrm{2}} +\mathrm{6}{r}+\mathrm{9}\right)\sqrt{{r}−\mathrm{1}}+\mathrm{16}{r}^{\mathrm{2}} +\mathrm{29}{r}+\mathrm{38}\right) \\ $$$${y}=\mathrm{16}\left(\mathrm{4}\left({r}^{\mathrm{2}}…