Question Number 64443 by mathmax by abdo last updated on 18/Jul/19 $${find}\:{all}\:{functin}\:{f}\:{Z}\rightarrow{Z}\:\:{wich}\:{verify} \\ $$$$\forall\left({a},{b}\right)\in{Z}^{\mathrm{2}} \:\:\:\:\:{f}\left(\mathrm{2}{a}\right)+\mathrm{2}{f}\left({b}\right)\:={f}\left({f}\left({a}+{b}\right)\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64355 by turbo msup by abdo last updated on 17/Jul/19 $${let}\:{F}\left({x}\right)=\int_{{u}\left({x}\right)} ^{{v}\left({x}\left\{\right.\right.} {f}\left({x},{t}\right){dt} \\ $$$${how}\:{to}\:{calculate}\:\:\frac{{dF}}{{dx}}\left({x}\right)? \\ $$ Commented by MJS last updated on…
Question Number 129873 by Bird last updated on 20/Jan/21 $${let}\:{m}={inff}\left({x}\right)_{{x}\in\left[{a},{b}\right]} \\ $$$${and}\:{M}={supf}\left({x}\right)_{{x}\in\left[{a},{b}\right]} \\ $$$${prove}\:{that}\:\left({b}−{a}\right)^{\mathrm{2}} \leqslant\int_{{a}} ^{{b}} {f}\left({x}\right){dx}.\int_{{a}} ^{{b}} \:\frac{{dx}}{{f}\left({x}\right)} \\ $$$$\leqslant\left({b}−{a}\right)^{\mathrm{2}} ×\frac{\left({m}+{M}\right)^{\mathrm{2}} }{\mathrm{4}{mM}} \\ $$…
Question Number 129872 by Bird last updated on 20/Jan/21 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{n}−{k}}{{n}^{\mathrm{2}} \:+{nk}+\mathrm{2009}} \\ $$$${determine}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 129870 by Bird last updated on 20/Jan/21 $${f}\:{continue}\:{on}\:\left[\bar {\mathrm{0}1}\right]\:{calculate} \\ $$$${lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}} \left({n}−{k}\right)\int_{\frac{{k}}{{n}}} ^{\frac{{k}+\mathrm{1}}{{n}}} {f}\left({x}\right){dx} \\ $$ Terms of Service Privacy Policy…
Question Number 129869 by Bird last updated on 20/Jan/21 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{\left.\:\sqrt{\left({k}+{n}\right)\left({k}+\mathrm{1}+{n}\right.}\right)} \\ $$ Answered by mindispower last updated on 20/Jan/21 $$ \\ $$$$\frac{\mathrm{1}}{\left({k}+\mathrm{1}+{n}\right)}\leqslant\frac{\mathrm{1}}{\:\sqrt{{k}+{n}}.\sqrt{{k}+\mathrm{1}+{n}}}\leqslant\frac{\mathrm{1}}{{k}+{n}}…\mathrm{1}…
Question Number 64300 by mathmax by abdo last updated on 16/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129403 by bemath last updated on 15/Jan/21 $$\:\mathrm{f}\left(\mathrm{n}\right)\:=\:\mathrm{4f}\left(\mathrm{n}−\mathrm{1}\right)\:−\mathrm{4f}\left(\mathrm{n}−\mathrm{2}\right)\:+\:\mathrm{n}^{\mathrm{2}} \: \\ $$$$\mathrm{and}\:\mathrm{f}\left(\mathrm{0}\right)=\mathrm{2}\:,\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{5}\: \\ $$ Commented by talminator2856791 last updated on 15/Jan/21 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{question}? \\ $$…
Question Number 129383 by mathmax by abdo last updated on 15/Jan/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{u}_{\mathrm{n}} \:\mathrm{wish}\:\mathrm{verify}\:\mathrm{u}_{\mathrm{n}−\mathrm{p}} +\mathrm{u}_{\mathrm{n}+\mathrm{p}} =\frac{\left(−\mathrm{1}\right)^{\mathrm{p}} }{\mathrm{n}+\mathrm{p}} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{n}\geqslant\mathrm{p} \\ $$ Terms of Service Privacy Policy…
Question Number 129336 by bramlexs22 last updated on 15/Jan/21 $$\mathrm{If}\:{a},{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$${x}^{\mathrm{3}} −\mathrm{21}{x}−\mathrm{35}\:=\:\mathrm{0}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\left({a}−{b}\right)\left({c}−{a}\right)\left({b}−{c}\right)\:? \\ $$ Commented by MJS_new last updated on 22/Jan/21 $${x}^{\mathrm{3}}…