Question Number 6028 by FilupSmith last updated on 10/Jun/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{show}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve}: \\ $$$${L}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}^{{n}} }{{n}!} \\ $$ Commented by Yozzii last updated on 10/Jun/16 $${Assume}\:{x}>\mathrm{0}. \\…
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Question Number 6027 by FilupSmith last updated on 10/Jun/16 $${x}^{{x}} ={e}^{{x}\mathrm{ln}\:{x}} \\ $$$${e}^{{x}} =\mathrm{1}+{x}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}+… \\ $$$$\therefore\:{e}^{{x}\mathrm{ln}\:{x}} \:=\:\mathrm{1}+{x}\mathrm{ln}\left({x}\right)+\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{2}} }{\mathrm{2}!}+… \\ $$$${e}^{{x}\mathrm{ln}\:{x}} \:=\:\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{0}} }{\mathrm{0}!}+\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{1}} }{\mathrm{1}!}+\frac{\left({x}\mathrm{ln}\:{x}\right)^{\mathrm{2}}…
Question Number 71563 by gunawan last updated on 17/Oct/19 $$\mathrm{find}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{cos}\:{x}+\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x} \\ $$$${for} \\ $$$$\frac{\pi}{\mathrm{6}}\leqslant{x}\leqslant\pi \\ $$ Answered by MJS last updated on 17/Oct/19…
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Question Number 137093 by mnjuly1970 last updated on 29/Mar/21 $$\:\:\:\:\:\:\:\:\:…..{advanced}\:\:\:\:{calculus}…. \\ $$$$\:\:\:\:\:{please}\:\:{evaluate}::\:\: \\ $$$$\:\:\:\:\:\mathrm{1}:\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\:=? \\ $$$$\:\:\:\:\mathrm{2}:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{xln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}−{x}}{dx}=? \\ $$$$\:\:{note}:{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{n}}=\int_{\mathrm{0}}…
Question Number 6021 by sanusihammed last updated on 10/Jun/16 $$\mathrm{2}^{{x}} \:+\:\mathrm{2}{x}\:=\:\mathrm{8}\: \\ $$$$ \\ $$$${find}\:{the}\:{value}\:{of}\:{x} \\ $$ Commented by Yozzii last updated on 10/Jun/16 $${x}=\mathrm{2}…
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Question Number 6016 by sanusihammed last updated on 09/Jun/16 $$\int\left(\frac{\mathrm{2}{x}\:+\:\mathrm{5}}{\:\sqrt{\mathrm{3}\:+\:\mathrm{4}{x}\:−\:\mathrm{5}{x}^{\mathrm{2}} }}\right){dx} \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Answered by Yozzii last updated on 09/Jun/16 $${Let}\:{u}=\mathrm{3}+\mathrm{4}{x}−\mathrm{5}{x}^{\mathrm{2}}…