Question Number 129052 by oustmuchiya@gmail.com last updated on 12/Jan/21 $${Let}\:\boldsymbol{\mathrm{p}}\:{and}\:\boldsymbol{\mathrm{Q}}\:{be}\:{points}\:{on}\:{the}\:{curve} \\ $$$$\boldsymbol{{y}}=\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}\:{while}\:\boldsymbol{{x}}=\mathrm{2}\:{and}\:\boldsymbol{{x}}=\mathrm{2}+\boldsymbol{{h}} \\ $$$$\boldsymbol{{respectively}}.\:\boldsymbol{{E}}{press}\:{the}\:{gradient} \\ $$$${of}\:\boldsymbol{\mathrm{P}}{Q}\:{in}\:{terms}\:{of}\:\boldsymbol{{h}}. \\ $$ Commented by benjo_mathlover last updated on…
Question Number 128951 by mathmax by abdo last updated on 11/Jan/21 $$\mathrm{solve}\:\mathrm{y}^{,,} −\mathrm{2y}^{'} \:+\mathrm{3y}\:=\mathrm{xe}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{2x}\right)\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$ Answered by mnjuly1970 last updated on 11/Jan/21…
Question Number 63389 by mathmax by abdo last updated on 03/Jul/19 $${f}\:{function}\:{integrable}\:{on}\:\left[{a},{b}\right] \\ $$$${is}\:{max}\:\int_{{a}} ^{{b}} {f}\left({x}\right){dx}\:=\int_{{a}} ^{{b}} \:{maxf}\left({x}\right){dx}?\:\:{if}\:{not}\:{give}\:{a}\:{opposite}\:{example}\:. \\ $$ Commented by MJS last updated…
Question Number 63215 by mathmax by abdo last updated on 30/Jun/19 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \left\{{n}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} −{en}\right\} \\ $$ Commented by mathmax by abdo last updated on 01/Jul/19…
Question Number 63165 by mathmax by abdo last updated on 29/Jun/19 $${let}\:{W}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:\:\:{determine}\:{W}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$${H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Terms of…
Question Number 63164 by mathmax by abdo last updated on 29/Jun/19 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\:\:\:\:\:{and}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$$${calculate}\:{S}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}}…
Question Number 63101 by mathmax by abdo last updated on 29/Jun/19 $${calculate}\:\:{S}\:=\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}}\:+….. \\ $$ Commented by mathmax by abdo last updated on 29/Jun/19 $${let}\:{try}\:{another}\:{way}\:{we}\:{have}\:\frac{{d}}{{dx}}{ln}\left(\mathrm{1}+{x}\right)\:=\frac{\mathrm{1}}{\mathrm{1}+{x}}\:=\sum_{{n}=\mathrm{0}} ^{\infty}…
Question Number 128498 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{simplify}\:\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i}\right)^{\mathrm{n}} }+\frac{\mathrm{1}}{\left(\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{i}\right)^{\mathrm{n}} } \\ $$ Answered by TheSupreme last updated on 08/Jan/21 $$\mathrm{1}+{i}\sqrt{\mathrm{3}}=\mathrm{2}{e}^{{i}\frac{\pi}{\mathrm{3}}}…
Question Number 62962 by fyyac c last updated on 27/Jun/19 $${P}\left({x}\right)=\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{1}}\: \\ $$$${P}_{\mathrm{1000}} \left({x}\right)=?\:{what}\:{is}\:{this}\:{sum}\:{in}\:{terms}\:{of}\:{x}? \\ $$ Terms of Service Privacy…
Question Number 128497 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{calvulate}\:\mathrm{A}\:=\frac{\mathrm{1}}{\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)^{\mathrm{6}} }+\frac{\mathrm{1}}{\left(\sqrt{\mathrm{3}}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com