Question Number 192227 by sonukgindia last updated on 12/May/23 Answered by senestro last updated on 12/May/23 $$…\mathrm{76} \\ $$ Commented by text last updated on…
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Question Number 192220 by gatocomcirrose last updated on 12/May/23 $$ \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{if}\:\mathrm{n}\in\mathbb{N},\:\mathrm{n}>\mathrm{1}\:\mathrm{and}\:\mathrm{n}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{then} \\ $$$$\:\mathrm{1}^{\mathrm{n}} +…+\left(\mathrm{n}−\mathrm{1}\right)^{\mathrm{n}} \:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{n} \\ $$$$\left(\mathrm{dont}\:\mathrm{use}\:\equiv\left(\mathrm{modn}\right)\right) \\ $$ Commented by AST last updated…
Question Number 126685 by bramlexs22 last updated on 23/Dec/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}\:\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}{{x}\:\mathrm{sin}\:{x}}\:=? \\ $$ Answered by liberty last updated on 23/Dec/20 $$\:\left(\ast\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}\:\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}{{x}\:\mathrm{sin}\:{x}}\:= \\ $$$$\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}}…
Question Number 126682 by bramlexs22 last updated on 23/Dec/20 $$\:{Find}\:{the}\:{remainder}\: \\ $$$$\:\mathrm{7}+\mathrm{77}+\mathrm{777}+\mathrm{7777}+…+\underset{\mathrm{2020}\:{times}} {\underbrace{\mathrm{777}…\mathrm{7}}} \\ $$$${when}\:{divided}\:{by}\:\mathrm{9}. \\ $$ Answered by talminator2856791 last updated on 23/Dec/20 $$\:…
Question Number 61147 by malwaan last updated on 29/May/19 $$\boldsymbol{{prove}} \\ $$$$\int\frac{\mathrm{1}+{cos}\:{x}}{\mathrm{1}−{cos}\:{x}}{dx}=−\mathrm{2}{cot}\:\frac{{x}}{\mathrm{2}}−{x}+{c} \\ $$$$ \\ $$ Answered by tanmay last updated on 29/May/19 $$\int\frac{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 126683 by bramlexs22 last updated on 23/Dec/20 $$\:{solve}\:\left({D}^{\mathrm{2}} +{a}\right){y}\:=\:\mathrm{tan}\:{ax}\: \\ $$ Answered by liberty last updated on 23/Dec/20 $$\left(\mathrm{1}\right)\:{Homogenous}\:{solution} \\ $$$$\:{y}_{{h}} =\:{A}\:\mathrm{cos}\:{ax}\:+\:{B}\:\mathrm{sin}\:{ax}\: \\…
Question Number 192212 by josemate19 last updated on 11/May/23 $$\int−\mathrm{1}^{{x}} {dx} \\ $$ Answered by Frix last updated on 12/May/23 $$\int−\mathrm{1}^{{x}} {dx}=−\int\mathrm{1}^{{x}} {dx}=−\int{dx}=−{x}+{C} \\ $$$$\int\left(−\mathrm{1}\right)^{{x}}…
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