Question Number 68354 by TawaTawa last updated on 09/Sep/19 $$\underset{{x},\mathrm{y}\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{4}} \:−\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{4}} \mathrm{y}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{2}} } \\ $$ Commented by kaivan.ahmadi last…
Question Number 2818 by prakash jain last updated on 27/Nov/15 $$\mathrm{show}\:\mathrm{that} \\ $$$$\Gamma'\left(\mathrm{1}\right)=−\gamma \\ $$$$\Gamma\:\mathrm{gamma}\:\mathrm{function} \\ $$$$\gamma=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[\mathrm{H}_{{n}} −\mathrm{ln}\:{n}\right] \\ $$ Answered by 123456 last…
Question Number 133885 by bemath last updated on 25/Feb/21 $$\:\mathrm{Consider}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{intersecting}\:\mathrm{straight}\:\mathrm{lines} \\ $$$$\begin{cases}{{ax}+{by}+{c}=\mathrm{0}}\\{{a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} =\mathrm{0}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{a}\:\mathrm{given}\:\mathrm{point} \\ $$$$\left(\mathrm{x}_{\mathrm{0}} ,\mathrm{y}_{\mathrm{0}} \right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{point}…
Question Number 68350 by mhmd last updated on 09/Sep/19 Commented by MJS last updated on 09/Sep/19 $$\left({x}−\mathrm{2cos}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\left({x}−\mathrm{2cos}\:\frac{\mathrm{4}\pi}{\mathrm{7}}\right)\left({x}−\mathrm{cos}\:\frac{\mathrm{6}\pi}{\mathrm{7}}\right)=\mathrm{0} \\ $$$$\mathrm{approximating}\:\mathrm{leads}\:\mathrm{to} \\ $$$${x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that}…
Question Number 2815 by prakash jain last updated on 28/Nov/15 $$\eta\left({s}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{{s}} }\:\mathrm{Dirichlet}\:\mathrm{eta}\:\mathrm{function} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\eta\left({s}\right)=\left(\mathrm{1}−\mathrm{2}^{\mathrm{1}−{s}} \right)\zeta\left({s}\right) \\ $$ Commented by prakash…
Question Number 133887 by bemath last updated on 25/Feb/21 $$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:;\:\mathrm{y}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 68349 by peter frank last updated on 09/Sep/19 Answered by mr W last updated on 09/Sep/19 $${w}_{{new}} =\mathrm{1}.\mathrm{03}{w}\:\:\:\left(\mathrm{3\%}\:{more}={factor}\:\mathrm{1}.\mathrm{03}\right) \\ $$$${d}_{{new}} =\mathrm{0}.\mathrm{975}{d}\:\:\:\left(\mathrm{2}.\mathrm{5\%}\:{less}={factor}\:\mathrm{0}.\mathrm{975}\right) \\ $$$${t}_{{new}}…
Question Number 68346 by peter frank last updated on 09/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 68342 by Tony Lin last updated on 09/Sep/19 Commented by Tony Lin last updated on 09/Sep/19 $${when}\:{m}\:{slide}\:{to}\:{the}\:{bottom} \\ $$$${if}\:{there}\:{is}\:{no}\:{fraction} \\ $$$${find}\:{v}_{{m}} \&{v}_{{M}} \\…
Question Number 2806 by prakash jain last updated on 27/Nov/15 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{cos}\:{ix}}{{i}^{\mathrm{2}} }\:\mathrm{is}\:\mathrm{uniformly}\:\mathrm{convergent}\:\mathrm{on}\:\mathrm{real}\:\mathrm{line}. \\ $$ Answered by Yozzi last updated on 27/Nov/15…