Question Number 200747 by Rupesh123 last updated on 22/Nov/23 Answered by MM42 last updated on 22/Nov/23 $$\left.{lnx}={u}\Rightarrow\int_{\mathrm{1}} ^{\infty} \:\frac{{du}}{{u}^{\mathrm{2}} }\:=−\frac{\mathrm{1}}{{u}}\right]_{\mathrm{1}} ^{\infty} =\mathrm{1}\:\checkmark \\ $$ Commented…
Question Number 200736 by Calculusboy last updated on 22/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{A}}\:\boldsymbol{{particle}}\:\boldsymbol{{moves}}\:\boldsymbol{{along}}\:\boldsymbol{{the}}\:\boldsymbol{{space}} \\ $$$$\boldsymbol{{curve}}\:\underset{−} {\boldsymbol{{r}}}=\left(\boldsymbol{{t}}^{\mathrm{2}} +\boldsymbol{{t}}\right)\boldsymbol{{i}}+\left(\mathrm{3}\boldsymbol{{t}}−\mathrm{2}\right)\boldsymbol{{j}}+\left(\mathrm{2}\boldsymbol{{t}}^{\mathrm{3}} −\mathrm{4}\boldsymbol{{t}}^{\mathrm{2}} \right)\boldsymbol{{k}}. \\ $$$$\boldsymbol{{find}} \\ $$$$\left(\boldsymbol{{a}}\right)\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{b}}\right)\boldsymbol{{speed}}\:\boldsymbol{{or}}\:\boldsymbol{{magnitude}}\:\boldsymbol{{of}}\:\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{c}}\right)\boldsymbol{{acceleration}} \\…
Question Number 200737 by Calculusboy last updated on 22/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{The}}\:\boldsymbol{{position}}\:\boldsymbol{{vector}}\:\boldsymbol{{of}}\:\boldsymbol{{a}}\:\boldsymbol{{particle}}\:\boldsymbol{{at}}\:\boldsymbol{{any}}\:\boldsymbol{{time}}\:\boldsymbol{{t}} \\ $$$$\boldsymbol{{is}}\:\boldsymbol{{given}}\:\boldsymbol{{by}}\:\:\underset{−} {\boldsymbol{{r}}}=\left(\boldsymbol{{acoswt}}\right)\boldsymbol{{i}}+\left(\boldsymbol{{asinwt}}\right)\boldsymbol{{j}}+\boldsymbol{{bt}}^{\mathrm{2}} \boldsymbol{{k}} \\ $$$$\left(\boldsymbol{{a}}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}},\boldsymbol{{although}}\:\boldsymbol{{the}}\:\boldsymbol{{speed}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{particle}} \\ $$$$\boldsymbol{{increases}}\:\boldsymbol{{with}}\:\boldsymbol{{time}},\boldsymbol{{the}}\:\boldsymbol{{magnitude}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{acceleration}}\:\boldsymbol{{is}}\:\boldsymbol{{always}}\:\boldsymbol{{constant}} \\ $$$$\left(\boldsymbol{{b}}\right)\:\boldsymbol{{describe}}\:\boldsymbol{{the}}\:\boldsymbol{{motion}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{particle}}\:\boldsymbol{{geometrically}} \\ $$ Terms…
Question Number 200684 by Spillover last updated on 21/Nov/23 $$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{−\mathrm{4}\pi} ^{\mathrm{4}\pi} \:\:\:\frac{\mid{x}\mid\:\mathrm{sin}\:^{\mathrm{2}{n}} {x}}{\mathrm{sin}\:^{\mathrm{2}{n}} {x}+\mathrm{cos}\:^{\mathrm{2}{n}} {x}}{dx} \\ $$$$ \\ $$$$ \\ $$ Answered by…
Question Number 200685 by Spillover last updated on 21/Nov/23 $$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\:\left(\mathrm{1}+\mathrm{tan}{x}\right){dx}\: \\ $$$$ \\ $$ Answered by som(math1967) last updated on 22/Nov/23…
Question Number 200569 by Rupesh123 last updated on 20/Nov/23 Answered by MM42 last updated on 20/Nov/23 $$\bigstar\:\:{e}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}!}\:\Rightarrow\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}!}={e}−\mathrm{2} \\ $$$$\sqrt{{x}\sqrt[{\mathrm{3}}]{{x}\sqrt[{\mathrm{4}}]{{x}\sqrt[{\mathrm{5}}]{\sqrt{{x}…}}}}}={x}^{\frac{\mathrm{1}}{\mathrm{2}}} ×{x}^{\frac{\mathrm{1}}{\mathrm{6}}} ×{x}^{\frac{\mathrm{1}}{\mathrm{24}}}…
Question Number 200570 by Rupesh123 last updated on 20/Nov/23 Answered by witcher3 last updated on 20/Nov/23 $$\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{sin}\left(\mathrm{n}\right)}{\mathrm{n}}=\mathrm{Im}\left\{\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{e}^{\mathrm{in}} }{\mathrm{n}}\right\} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{N}} {\sum}}\mathrm{e}^{\mathrm{in}} =\frac{\mathrm{e}^{\mathrm{i}}…
Question Number 200553 by cortano12 last updated on 20/Nov/23 $$\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 200604 by Calculusboy last updated on 20/Nov/23 Commented by Frix last updated on 21/Nov/23 $$\mathrm{Does}\:\mathrm{not}\:\mathrm{converge}. \\ $$ Commented by Calculusboy last updated on…
Question Number 200605 by Calculusboy last updated on 20/Nov/23 Commented by Frix last updated on 21/Nov/23 $$\mathrm{Simply}\:\mathrm{integrate}\:\mathrm{by}\:\mathrm{parts}\:\mathrm{to}\:\mathrm{get} \\ $$$$\mathrm{ln}\:\mid\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\mid\:−\frac{{x}}{\mathrm{sin}\:{x}}+{C} \\ $$ Commented by Calculusboy last…