Question Number 203835 by patrice last updated on 29/Jan/24 Answered by MathematicalUser2357 last updated on 30/Jan/24 $${bruh} \\ $$ Commented by Frix last updated on…
Question Number 203063 by LowLevelLump last updated on 09/Jan/24 Answered by MM42 last updated on 09/Jan/24 $${f}'={e}^{{x}} −{a}=\mathrm{0}\Rightarrow\alpha={lna} \\ $$$$\Rightarrow{minf}={a}−{alna} \\ $$$$\:{g}'={a}−\frac{\mathrm{1}}{{x}}=\mathrm{0}\Rightarrow\beta=\frac{\mathrm{1}}{{a}} \\ $$$$\Rightarrow{ming}=\mathrm{1}+{lna} \\…
Question Number 202866 by mnjuly1970 last updated on 04/Jan/24 $$ \\ $$$$\:\:\:\:\:\:\:{calculate}\:… \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{\:−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}\:+\:{x}\:\right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by Mathspace…
Question Number 201940 by Calculusboy last updated on 15/Dec/23 $$\boldsymbol{{tan}}^{\mathrm{3}} \left(\boldsymbol{{xy}}^{\mathrm{2}} +\boldsymbol{{y}}\right)=\boldsymbol{{x}}\:\:\boldsymbol{{find}}\:\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}} \\ $$ Answered by cortano12 last updated on 16/Dec/23 $$\:\:\Rightarrow\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\mathrm{tan}\:^{\mathrm{3}} \left(\mathrm{xy}^{\mathrm{2}} +\mathrm{y}\right)\:\right]\:=\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}\right) \\…
Question Number 201534 by Mathspace last updated on 08/Dec/23 $${let}\:{f}\left({x}\right)={tanx} \\ $$$${find}\:{f}^{\left({n}\right)} \left({x}\right)\:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$ Commented by Frix last updated on 09/Dec/23 $$\mathrm{There}'\mathrm{s}\:\mathrm{a}\:\mathrm{very}\:\mathrm{complicated}\:\mathrm{formula},\:\mathrm{you}\:\mathrm{must}…
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Question Number 201214 by mr W last updated on 02/Dec/23 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{function}\:{z}={xy}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{2},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{the}\:{xy}−\mathrm{plane}\:\mathrm{where}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{will} \\ $$$$\mathrm{touch}\:\mathrm{it}. \\ $$$$ \\ $$$$\left({an}\:{unsolved}\:{old}\:{question}\:{Q}\mathrm{200929}\right) \\ $$ Answered by…
Question Number 201140 by Calculusboy last updated on 30/Nov/23 $$\boldsymbol{{If}}\:\underset{−} {\boldsymbol{{R}}}=\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}\underset{−} {\boldsymbol{{i}}}−\mathrm{2}\boldsymbol{{y}}^{\mathrm{2}} \boldsymbol{{z}}\underset{−} {\boldsymbol{{j}}}+\boldsymbol{{xy}}^{\mathrm{2}} \boldsymbol{{z}}^{\mathrm{2}} \underset{−} {\boldsymbol{{k}}},\:\boldsymbol{{find}}\:\mid\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dx}}^{\mathrm{2}} }×\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dy}}^{\mathrm{2}} }\mid\:\: \\ $$$$\boldsymbol{{at}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\left(\mathrm{2},\mathrm{1},−\mathrm{2}\right) \\…
Question Number 201133 by mnjuly1970 last updated on 30/Nov/23 $$ \\ $$$$ \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{1}} ^{\:\mathrm{3}} \frac{\:\mathrm{1}}{\:\sqrt{\left({x}−\mathrm{1}\:\right)^{\mathrm{3}} }\:+\:\sqrt{\left({x}+\mathrm{1}\:\right)^{\mathrm{3}} }}\:{dx}=\:?\:\:\: \\ $$$$ \\ $$ Commented by Frix…
Question Number 200738 by Calculusboy last updated on 22/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{A}}\:\boldsymbol{{smooth}}\:\boldsymbol{{sphere}}\:\boldsymbol{{A}},\boldsymbol{{of}}\:\boldsymbol{{mass}}\:\mathrm{2}\boldsymbol{{kg}}\:\boldsymbol{{and}} \\ $$$$\boldsymbol{{moving}}\:\boldsymbol{{with}}\:\boldsymbol{{speed}}\:\mathrm{6}\boldsymbol{{ms}}^{−\mathrm{1}} \boldsymbol{{collides}}\:\boldsymbol{{obliquely}}\: \\ $$$$\boldsymbol{{with}}\:\boldsymbol{{a}}\:\boldsymbol{{smooth}}\:\boldsymbol{{sphere}}\:\boldsymbol{{B}}\:\boldsymbol{{of}}\:\boldsymbol{{mass}}\:\mathrm{4}\boldsymbol{{kg}}.\:\boldsymbol{{just}}\:\boldsymbol{{before}}\:\boldsymbol{{the}}\:\boldsymbol{{impact}}\:\boldsymbol{{B}}\:\boldsymbol{{is}} \\ $$$$\boldsymbol{{stationary}}\:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{velocity}}\:\boldsymbol{{of}}\:\boldsymbol{{A}}\:\boldsymbol{{makes}} \\ $$$$\boldsymbol{{an}}\:\boldsymbol{{angle}}\:\boldsymbol{{of}}\:\mathrm{10}°\:\boldsymbol{{with}}\:\boldsymbol{{the}}\:\boldsymbol{{lines}}\:\boldsymbol{{of}}\:\boldsymbol{{centers}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{two}}\:\boldsymbol{{sphere}}. \\ $$$$\boldsymbol{{The}}\:\boldsymbol{{coefficient}}\:\boldsymbol{{of}}\:\boldsymbol{{restitution}}\:\boldsymbol{{between}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{spheres}}\:\boldsymbol{{is}}\:\frac{\mathrm{1}}{\mathrm{2}}.\:\boldsymbol{{Find}}\:\boldsymbol{{the}}\:\boldsymbol{{magnitude}}\:\boldsymbol{{and}}\: \\ $$$$\boldsymbol{{directions}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{velovities}}\:\boldsymbol{{of}}\:\boldsymbol{{A}}\:\boldsymbol{{and}}\:\boldsymbol{{B}}…