Question Number 192867 by beto last updated on 30/May/23 $${derivate}\:{of}\:\:{csc}\left(\mathrm{2}{x}\right)\:{by}\:\:{definition} \\ $$ Answered by cortano12 last updated on 02/Jun/23 $$\:\frac{\mathrm{d}\left(\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{2x}}\right)}{\mathrm{dx}}=\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}}{\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{2h}\right)}−\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{2x}}}{\mathrm{h}} \\ $$$$\:=\:\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}−\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{2h}\right)}{\mathrm{h}\:\mathrm{sin}\:\mathrm{2x}\:\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{2h}\right)} \\…
Question Number 61791 by naka3546 last updated on 08/Jun/19 $$\underset{{x}\:\rightarrow\:\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{6}^{{x}} }{\mathrm{2}^{{x}} \:+\:\mathrm{4}^{{x}} }\:\:\:=\:\:\:\infty\:\:\:\:\:? \\ $$ Commented by mr W last updated on 08/Jun/19 $$\underset{{x}\:\rightarrow\:\infty}…
Question Number 192862 by Red1ight last updated on 30/May/23 $$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{115}{x}+\mathrm{150}=\mathrm{0} \\ $$ Answered by Frix last updated on 30/May/23 $$\left({x}−\mathrm{10}\right)\left({x}^{\mathrm{2}} +\mathrm{10}{x}−\mathrm{15}\right)=\mathrm{0} \\…
Question Number 127322 by MathSh last updated on 28/Dec/20 $${f}\left({x}\right)\:{function}\:{pair}\:{and}\:\left(−\infty;\mathrm{0}\right] \\ $$$${decreases}\:{in}\:{the}\:{range} \\ $$$${f}\left({x}\right)\geqslant{f}\left(−\mathrm{3}\right)\:{solve}\:{the}\:{inequality} \\ $$ Answered by mindispower last updated on 28/Dec/20 $$\left.\right]\left.−\infty,−\mathrm{3}\right]\cup\left[\mathrm{3},+\infty\left[\right.\right. \\…
Question Number 192856 by universe last updated on 29/May/23 $$\:{if}\:{a}+{b}+{c}\:+{d}\:\:=\:\mathrm{63}\:{and}\:{a},{b},{c},{d}\:\in\:\mathbb{N}\:{find}\: \\ $$$$\:\:\:{the}\:{maximum}\:{value}\:{of}\:{ab}+{bc}+{cd}\:=\:? \\ $$ Answered by Frix last updated on 29/May/23 $$\mathrm{32}+\mathrm{31}+\mathrm{0}+\mathrm{0}=\mathrm{63} \\ $$$$\mathrm{32}×\mathrm{31}=\mathrm{992} \\…
Question Number 61785 by aliesam last updated on 08/Jun/19 $$\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{3}−{x}^{\mathrm{2}} }} {\int}}\frac{{xy}\left(\mathrm{4}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }−{xy}}{\mathrm{3}}\:{dy} \\ $$ Answered by MJS last updated on…
Question Number 192858 by josemate19 last updated on 29/May/23 $$\int_{\mathrm{4}{x}} ^{\:{x}^{\mathrm{3}} } \sqrt{\sqrt{{t}}+{t}^{\mathrm{1}/\mathrm{3}} }{dt} \\ $$ Answered by Frix last updated on 29/May/23 $$\int\sqrt{\sqrt{{t}}+\sqrt[{\mathrm{3}}]{{t}}}{dt}= \\…
Question Number 192852 by York12 last updated on 29/May/23 $$ \\ $$$${find}\:{the}\:{domain}\:{of}\:{thefunction} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\left\{{x}\right\}^{\mathrm{2}} }}\:\:\:\:\:{where}\:\left\{.\right\}\:{is}\:{the}\:{fractional}\:{part}\:{function}. \\ $$ Commented by York12 last updated on 30/May/23…
Question Number 61782 by naka3546 last updated on 08/Jun/19 $${Any}\:\:{integer}\left({s}\right)\:\:{which}\:\:{fulfill} \\ $$$$\:\:\:\:\:\:\:\:\:\:{n}^{\mathrm{5}} \:−\:\mathrm{5}{n}^{\mathrm{3}} \:+\:\mathrm{5}{n}\:+\:\mathrm{1}\:\:\mid\:\:{n}!\:\:\:? \\ $$ Commented by naka3546 last updated on 08/Jun/19 $${please}\:\:{show}\:\:{workings}\:! \\…
Question Number 192855 by pascal889 last updated on 29/May/23 Answered by a.lgnaoui last updated on 29/May/23 $$\begin{cases}{\mathrm{P}^{\mathrm{2}} −\mathrm{2aP}−\mathrm{10P}+\mathrm{2a}^{\mathrm{2}} +\mathrm{6a}\:\:−\mathrm{6}=\mathrm{0}\:\:\left(\mathrm{1}\right)}\\{\mathrm{P}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{27P}\:\:\:\:\:\:\:\:\:+\mathrm{27a}−\mathrm{27}=\mathrm{0}\:\:\left(\mathrm{2}\right)\:}\end{cases} \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right)\Rightarrow\:\mathrm{2a}^{\mathrm{2}} −\mathrm{21a}+\mathrm{21}+\mathrm{P}\left(\mathrm{17}−\mathrm{2a}\right)=\mathrm{0} \\ $$$$…