Question Number 213369 by Frix last updated on 03/Nov/24 $$\mathrm{Old}\:\mathrm{question}\:\mathrm{203835} \\ $$$$\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{2}}} {\int}}\frac{\sqrt{\mathrm{6}−\sqrt{\mathrm{25}{x}^{\mathrm{4}} −\mathrm{50}{x}^{\mathrm{2}} +\mathrm{36}}}}{\:\sqrt{\mathrm{5}}}{dx}=? \\ $$ Commented by MathematicalUser2357 last updated on 06/Nov/24…
Question Number 213276 by thetpainghtun_111 last updated on 02/Nov/24 $$\mathrm{y}^{\mathrm{2}} \:=\:−\:\mathrm{4px} \\ $$$$\:\mathrm{At}\:\left(−\frac{\mathrm{1}}{\mathrm{3}},\mathrm{1}\right)\rightarrow\:\mathrm{1}=\:−\mathrm{4p}\:\left(−\:\frac{\mathrm{1}}{\mathrm{3}}\:−\:\mathrm{h}\right) \\ $$$$\:\mathrm{At}\:\left(−\frac{\mathrm{5}}{\mathrm{3}},\mathrm{2}\right)\rightarrow\:\mathrm{4}\:=\:−\mathrm{4p}\:\left(−\:\frac{\mathrm{5}}{\mathrm{3}}\:−\:\mathrm{h}\right) \\ $$$$\:\:\:\:\:\mathrm{4}\:=\:\frac{−\:\frac{\mathrm{5}}{\mathrm{3}}\:−\:\mathrm{h}}{−\:\frac{\mathrm{1}}{\mathrm{3}}\:−\:\mathrm{h}} \\ $$$$\:\:\:\:\frac{\mathrm{4}}{\mathrm{3}}\:+\:\mathrm{4h}\:=\:\frac{\mathrm{5}}{\mathrm{3}}\:+\:\mathrm{h}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3h}\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{h}\:=\:\frac{\mathrm{1}}{\mathrm{9}} \\ $$…
Question Number 213267 by MrGaster last updated on 02/Nov/24 $$ \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{+\infty} \frac{{x}−{x}^{\mathrm{2}} +{x}^{\mathrm{3}} −\ldots−{x}^{\mathrm{2018}} }{\left(\mathrm{1}+{x}\right)^{\mathrm{2021}} }{dx} \\ $$ Answered by TonyCWX08 last updated…
Question Number 213292 by MathematicalUser2357 last updated on 02/Nov/24 $${hey}\:{tinku}\:{tara} \\ $$$${I}\:{cant}\:{plot}\:{functions} \\ $$$${even}\:{i}\:{am}\:{logged}\:{in} \\ $$$${it}\:{says}\:{check}\:{if}\:{the}\:{variable}\:{name}\:{is}\:“{x}''\:{and}\:{you}\:{are}\:{logged}\:{in} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 213290 by issac last updated on 02/Nov/24 $$\mathrm{for}\:\mathrm{every}\:\mathrm{real}\:\mathrm{set}\:\mathbb{R}\:,\:{f}\in\mathbb{R} \\ $$$$\mathrm{and}\:{f}\:\mathrm{is}\:\mathrm{Smooth}\:\mathrm{function}.\:\mathrm{and}\:{f}\:\mathrm{is}\:{f}\in\mathcal{C}^{\mathrm{2}} \\ $$$$\forall_{{x}} \:{f}^{\left(\mathrm{1}\right)} \left({x}\right)>\mathrm{0}\:,\:{f}^{\left(\mathrm{2}\right)} \left({x}\right)<\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mid\int_{\mathrm{0}} ^{\:{t}} \:\mathrm{cos}\left({f}\left({x}\right)\right)\mathrm{d}{x}\mid\leq\frac{\mathrm{2}}{{f}^{\left(\mathrm{1}\right)} \left({t}\right)} \\ $$$${t}\in\mathbb{R} \\…
Question Number 213283 by issac last updated on 02/Nov/24 $${a}_{{h}} \:\mathrm{is}\:\mathrm{Cauchy}\:\mathrm{Sequence}. \\ $$$$\mathrm{Sequence}\:\left\{{a}_{{h}} \right\}_{{h}=\mathrm{1}} ^{{n}} \mathrm{Satisfy}\:\underset{{h}=\mathrm{1}} {\overset{{n}} {\sum}}\:{a}_{{h}} =\mathrm{0}\:,\:\underset{{h}=\mathrm{1}} {\overset{{n}} {\sum}}\:{a}_{{h}} ^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{Summation}…
Question Number 213208 by issac last updated on 01/Nov/24 $$\mathrm{Let}\:{f}\left({x}\right)\in\mathbb{Q}\left[{x}\right]\:\mathrm{irreducible}\:\mathrm{of}\:\mathrm{degree}\:{n} \\ $$$$\mathrm{and}\:{K}\:\mathrm{it}'\mathrm{s}\:\mathrm{Splitting}\:\mathrm{Field}\:\mathrm{over}\:\mathbb{Q} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\mathrm{Gal}\left({K}\backslash\mathbb{Q}\right)\:\mathrm{is}\:\mathrm{Abeilan} \\ $$$$\mathrm{then}\:\mid\mathrm{Gal}\left({K}\backslash\mathbb{Q}\right)\mid={n} \\ $$$$\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{prove}\:\mathrm{this}??? \\ $$ Answered by MrGaster last updated…
Question Number 213232 by Frix last updated on 01/Nov/24 $$\mathrm{Just}\:\mathrm{a}\:\mathrm{warning}:\:\mathrm{the}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{these}\:\mathrm{two} \\ $$$$\mathrm{here}\:\mathrm{are}\:\mathrm{very}\:\mathrm{often}\:\mathrm{wrong}: \\ $$$$ \\ $$$$\mathrm{MrGaster} \\ $$$$\mathrm{lepuissantcedricjunior} \\ $$$$ \\ $$$$\mathrm{They}\:\mathrm{also}\:\mathrm{do}\:\mathrm{not}\:\mathrm{answer}\:\left(\mathrm{my}\right)\:\mathrm{comments} \\ $$$$\mathrm{regarding}\:\mathrm{their}\:\mathrm{errors}. \\…
Question Number 213198 by Ismoiljon_008 last updated on 01/Nov/24 Answered by mr W last updated on 01/Nov/24 Commented by mr W last updated on 01/Nov/24…
Question Number 213175 by Davidtim last updated on 31/Oct/24 $${we}\:{can}\:{find}\:{tan}\mathrm{120}\:{by}\:{tan}\left(\mathrm{180}−\mathrm{60}\right) \\ $$$${but}\:{can}\:{not}\:{find}\:{by}\:{tan}\left(\mathrm{90}+\mathrm{30}\right)\:{why}? \\ $$ Answered by efronzo1 last updated on 31/Oct/24 $$\:\mathrm{tan}\:\mathrm{120}°=\:\mathrm{tan}\:\left(\mathrm{90}°+\mathrm{30}°\right)\:=−\:\mathrm{cot}\:\mathrm{30}°=−\sqrt{\mathrm{3}} \\ $$ Answered…