Question Number 73406 by Rio Michael last updated on 11/Nov/19 $${Use}\:{the}\:{Sandwich}\left(\:{Pinchin}\:{or}\:{Squeez}\:\right)\:{theorem}\:{to}\:{prove} \\ $$$${that}\: \\ $$$$\:\underset{{x}\rightarrow{a}} {\mathrm{Lim}}\:\sqrt{{x}}\:=\:\sqrt{{a}}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138940 by mnjuly1970 last updated on 20/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{mathematics}.. \\ $$$${prove}\:{that}: \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:=\frac{\pi^{\mathrm{2}} {ln}\left(\mathrm{2}\right)}{\mathrm{4}}+\frac{\mathrm{7}}{\mathrm{8}}\:\zeta\left(\mathrm{3}\right) \\ $$ Terms of…
Question Number 7869 by FilupSmith last updated on 22/Sep/16 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{numerical}\:\mathrm{value} \\ $$$$\mathrm{for}\:{x}\:\mathrm{in}: \\ $$$${xe}^{{x}} =\mathrm{1} \\ $$ Commented by FilupSmith last updated on 22/Sep/16 $${x}={W}\left({xe}^{{x}}…
Question Number 73405 by Rio Michael last updated on 11/Nov/19 $${can}\:{someone}\:{please}\:{prove}\:{the}\: \\ $$$${Chinese}\:{Remainder}\:{theorem},\:{for}\: \\ $$$${modula}\:{arithmetic}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138933 by mnjuly1970 last updated on 20/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 73399 by mathocean1 last updated on 11/Nov/19 $$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{65}}\\{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)=\mathrm{17}}\end{cases} \\ $$$$ \\ $$$${please}\:{help}\:{me}\:{to}\:{solve}\:{it}… \\ $$ Commented by abdomathmax last updated on 11/Nov/19…
Question Number 73396 by mathmax by abdo last updated on 11/Nov/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{t}^{\mathrm{2}} } {ln}\left(\mathrm{1}−{t}\right){dt} \\ $$ Commented by mathmax by abdo last updated…
Question Number 7861 by Yozzia last updated on 21/Sep/16 $${Prove}\:{that}\:\underset{{i}=\mathrm{0}} {\overset{{n}+\mathrm{1}} {\sum}}\begin{pmatrix}{{n}+\mathrm{1}}\\{{i}}\end{pmatrix}\:{i}^{{n}} \left(−\mathrm{1}\right)^{{i}+\mathrm{1}} =\mathrm{0}\: \\ $$$${for}\:\forall{n}\in\mathbb{N}. \\ $$ Commented by FilupSmith last updated on 22/Sep/16…
Question Number 73397 by mathmax by abdo last updated on 11/Nov/19 $${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{t}} {ln}\left(\mathrm{1}−{xt}^{\mathrm{2}} \right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{t}} {ln}\left(\mathrm{1}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}\right){dt} \\ $$ Commented…