Question Number 66016 by Rio Michael last updated on 07/Aug/19 $${Evaluate}\:\:\: \\ $$$${a}.\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\left({lnx}\right)^{\mathrm{2}} {dx} \\ $$$${b}.\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:{sin}^{\mathrm{2}} {x}\:{cos}^{\mathrm{3}} {xdx} \\ $$ Commented…
Question Number 481 by 123456 last updated on 12/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:\left\{{x}_{{n}} \right\}\:{is}\:{a}\:{no}\:{limited}\:{sequence} \\ $$$${then} \\ $$$${exist}\:{a}\:{sub}−{sequence}\:\left\{{x}_{{nk}} \right\}\:{that} \\ $$$$\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{{x}_{{nk}} }=\mathrm{0} \\ $$ Commented…
Question Number 131554 by Salman_Abir last updated on 06/Feb/21 Commented by EDWIN88 last updated on 06/Feb/21 $$\mathrm{A}−\mathrm{B}=\:\begin{bmatrix}{−\mathrm{2}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}}\\{\:\:\:\mathrm{2}\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{6}}\end{bmatrix} \\ $$$$\mathrm{A}×\mathrm{B}^{\mathrm{T}} \:=\:\begin{bmatrix}{\mathrm{2}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\:\mathrm{4}}\\{\mathrm{1}\:\:\:\:\:\mathrm{5}\:\:\:\:\:\:\mathrm{7}}\end{bmatrix}\begin{bmatrix}{\mathrm{4}\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{4}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{bmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\begin{bmatrix}{\mathrm{8}+\mathrm{6}+\mathrm{12}\:\:\:\:\:\:\:−\mathrm{2}+\mathrm{12}+\mathrm{4}}\\{\mathrm{4}+\mathrm{10}+\mathrm{21}\:\:\:\:\:\:−\mathrm{1}+\mathrm{20}+\mathrm{7}}\end{bmatrix} \\ $$ Terms…
Question Number 66017 by Rio Michael last updated on 07/Aug/19 $${show}\:{that}\:{the}\:{equation}\:{xe}^{{x}} =\mathrm{1}\:{has}\:{a}\:{root}\:{between}\:\mathrm{0}.\mathrm{5}\:{and}\:\mathrm{0}.\mathrm{6}\:{starting} \\ $$$${with}\:\mathrm{0}.\mathrm{55}\:{as}\:{a}\:{first}\:{approximate}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 480 by 123456 last updated on 11/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${for}\:{s}\in\left\{\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[\frac{\mathrm{1}}{{s}^{{i}} }−\frac{\left(−\mathrm{1}\right)^{{i}} }{{i}^{{s}} }\right]\leqslant\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{s}+\mathrm{1}}{{si}^{{s}} } \\ $$ Commented…
Question Number 131549 by liberty last updated on 06/Feb/21 $$\mathrm{slowly}\:\mathrm{integral}\: \\ $$$$\int\:\frac{\mathrm{sec}\:^{\mathrm{4}} \mathrm{x}}{\:\sqrt{\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}}}\:\mathrm{dx}\:=? \\ $$ Answered by rs4089 last updated on 06/Feb/21 $$\frac{\mathrm{2}{tan}^{\mathrm{2}} {x}−\mathrm{6}}{\mathrm{3}\sqrt{{tanx}}}+{c}\:\:\:\:\left\{{c}\:{is}\:{a}\:{constant}\right\}…
Question Number 131548 by liberty last updated on 06/Feb/21 $$\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{n}}\:\underset{\mathrm{0}} {\overset{\:\:\frac{\pi}{\mathrm{2}}} {\int}}\:\mathrm{cos}\:^{\mathrm{2n}+\mathrm{1}} \left(\theta\right)\:\mathrm{d}\theta\:=? \\ $$ Answered by rs4089 last updated on 06/Feb/21 $$\frac{\pi\sqrt{\pi}}{\mathrm{2}} \\…
Question Number 131551 by liberty last updated on 06/Feb/21 $$\mathrm{Use}\:\mathrm{Euler}\:\mathrm{method}\:\mathrm{to}\:\mathrm{estimate}\: \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{solution}\:\mathrm{at}\:\mathrm{given}\: \\ $$$$\mathrm{point}\:\mathrm{x}^{\ast} \:.\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{5xe}^{\mathrm{x}^{\mathrm{5}} } \:,\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1}\:,\mathrm{dx}=\mathrm{0}.\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{x}^{\ast} =\mathrm{1}. \\ $$ Terms of Service…
Question Number 131550 by liberty last updated on 06/Feb/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{4}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\:\mathrm{If}\:\int_{\mathrm{5}} ^{\mathrm{7}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\mathrm{T}\:;\:\int_{\mathrm{3}} ^{\mathrm{5}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\mathrm{L} \\ $$$$\mathrm{then}\:\int_{\mathrm{2}} ^{\mathrm{10}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=? \\ $$ Answered by talminator2856791…
Question Number 476 by 123456 last updated on 11/Jan/15 $${given}\:{a}_{{n}} \:{and}\:{b}_{{n}} \:{two}\:{real}\:{sequence} \\ $$$${can}\:{a}\:{serie}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{a}_{{n}} \:{and}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{b}_{{n}} \:{diverge} \\ $$$${but} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty}…