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Author: Tinku Tara

Find-domain-of-y-213291-y-213291-3-e-x-2-3x-2-x-6-log-3-4-x-2-1-4-

Question Number 213291 by MathematicalUser2357 last updated on 02/Nov/24 $${Find}\:{domain}\:{of}\:{y}_{\mathrm{213291}} : \\ $$$${y}_{\mathrm{213291}} =\frac{\mathrm{3}+{e}^{\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}{{x}−\mathrm{6}}} }{\mathrm{log}_{\frac{\mathrm{3}}{\mathrm{4}}} \sqrt{{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}}} \\ $$ Answered by MrGaster last updated…

a-h-is-Cauchy-Sequence-Sequence-a-h-h-1-n-Satisfy-h-1-n-a-h-0-h-1-n-a-h-2-1-find-minimum-value-of-Summation-a-1-a-n-h-1-n-1-a-h-a-h-1-korea-university-math-conte

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}…

Let-f-x-Q-x-irreducible-of-degree-n-and-K-it-s-Splitting-Field-over-Q-Prove-that-if-Gal-K-Q-is-Abeilan-then-Gal-K-Q-n-How-can-i-prove-this-

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…

lim-x-0-sin-x-tan-x-x-3-

Question Number 213241 by RoseAli last updated on 01/Nov/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}−\mathrm{tan}\:{x}}{{x}^{\mathrm{3}} } \\ $$ Answered by ajfour last updated on 01/Nov/24 $$=−\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{\mathrm{sin}\:{x}}{{x}}×\left(\frac{\mathrm{1}−\mathrm{cos}\:{x}}{\mathrm{4}\left(\frac{{x}}{\mathrm{2}}\right)^{\mathrm{2}} }\right)×\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\right\} \\…

Just-a-warning-the-solutions-of-these-two-here-are-very-often-wrong-MrGaster-lepuissantcedricjunior-They-also-do-not-answer-my-comments-regarding-their-errors-If-you-need-the-answers-to-these-q

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-213234

Question Number 213234 by ajfour last updated on 01/Nov/24 Commented by Ghisom last updated on 01/Nov/24 $$\mathrm{let}\:{r}=\mathrm{1} \\ $$$${P}\in\mathrm{circle}:\:{P}=\begin{pmatrix}{\mathrm{cos}\:\theta}\\{\mathrm{1}+\mathrm{sin}\:\theta}\end{pmatrix} \\ $$$$\mathrm{parabola}:\:{y}=\left(\frac{\mathrm{2}+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta}−\frac{{x}}{\mathrm{cos}^{\mathrm{2}} \:\theta}\right){x} \\ $$$$\mathrm{tan}\:\alpha=\frac{\mathrm{2}+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta} \\…

G-

Question Number 213203 by golsendro last updated on 01/Nov/24 $$\:\:\:\:\:\:\cancel{\underline{\underbrace{\mathscr{G}}}} \\ $$ Answered by lepuissantcedricjunior last updated on 01/Nov/24 $$\boldsymbol{{f}}\left(\boldsymbol{{xy}}\right)=\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{f}}\left(\boldsymbol{{y}}\right) \\ $$$$\boldsymbol{{f}}\left(\mathrm{10}\right)=\mathrm{14};\boldsymbol{{f}}\left(\mathrm{20}\right)=\mathrm{40} \\ $$$$\boldsymbol{{calculons}}\:\boldsymbol{{f}}\left(\mathrm{500}\right) \\…