Question Number 202468 by hardmath last updated on 27/Dec/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\:\infty} {\sum}}\:\frac{\mathrm{16}}{\mathrm{16n}^{\mathrm{2}} \:−\:\mathrm{8n}\:−\:\mathrm{3}}\:=\:?\:\:\:\:\:\mathrm{2}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\:\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{2n}^{\mathrm{3}} }\:=\:? \\ $$ Answered by Rasheed.Sindhi last…
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Question Number 202466 by Rydel last updated on 27/Dec/23 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{x}\sqrt{\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)}}{\mathrm{1}+{e}^{{x}−\mathrm{3}} } \\ $$ Answered by Mathspace last updated on 27/Dec/23 $$={lim}_{{x}\rightarrow+\infty} {xe}^{−{x}+\mathrm{3}} \sqrt{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 202392 by MATHEMATICSAM last updated on 26/Dec/23 $$\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{b}\:=\:\mathrm{0} \\ $$$$\mathrm{is}\:{p}\::\:{q}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\sqrt{\frac{{p}}{{q}}}\:+\:\sqrt{\frac{{q}}{{p}}}\:+\:\sqrt{\frac{{b}}{{a}}}\:=\:\mathrm{0}. \\ $$ Commented by MATHEMATICSAM last updated on 26/Dec/23 $$\mathrm{The}\:\mathrm{question}\:\mathrm{is}\:\mathrm{corrected}\:\mathrm{now}…
Question Number 202393 by sonukgindia last updated on 26/Dec/23 Answered by Mathspace last updated on 26/Dec/23 $${I}=\int_{\mathrm{0}} ^{\infty} \frac{{lnx}}{{a}+{bx}^{\mathrm{2}} }{dx}\:\:\:\:\:\:\:\:\:\left({a}>\mathrm{0},{b}>\mathrm{0}\right) \\ $$$${I}=\frac{\mathrm{1}}{{a}}\int_{\mathrm{0}} ^{\infty} \frac{{lnx}}{\mathrm{1}+\frac{{b}}{{a}}{x}^{\mathrm{2}} }{dx}\:\:\left(\sqrt{\frac{{b}}{{a}}}{x}={t}\right)…
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Question Number 202448 by Calculusboy last updated on 26/Dec/23 Answered by professorleiciano last updated on 27/Dec/23 $${Nao}\:{tem}\:{antiderivada}\:{elementar}. \\ $$ Answered by MathematicalUser2357 last updated on…
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Question Number 202418 by MathematicalUser2357 last updated on 26/Dec/23 $$\mathrm{Hard}\:\mathrm{integral} \\ $$$$\int\int\int\int\int\int\int\int\int\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{f}}&{{g}}&{{h}}\\{{j}}&{{k}}&{{l}}\end{vmatrix}{dl}\:{dk}\:{dj}\:{dh}\:{dg}\:{df}\:{dc}\:{db}\:{da}= \\ $$ Answered by Frix last updated on 26/Dec/23 $$\mathrm{Not}\:\mathrm{hard}\:\mathrm{at}\:\mathrm{all} \\ $$$$=\frac{{abcfghjkl}}{\mathrm{8}}\left({a}\left({gl}−{hk}\right)−{b}\left({fl}−{hj}\right)+{c}\left({fk}−{gj}\right)\right) \\…
Question Number 202419 by MathematicalUser2357 last updated on 26/Dec/23 $$\mathrm{Hard}\:\mathrm{integral}:\:\mathrm{Q202393} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com