Menu Close

Author: Tinku Tara

Question-199922

Question Number 199922 by Mingma last updated on 11/Nov/23 Answered by AST last updated on 11/Nov/23 $${WLOG},{let}\:{C}\:{be}\:{the}\:{origin}\:{and}\:{let}\:{AD}\:{coincide} \\ $$$${with}\:{the}\:{real}\:{axis};{then}\:{a}=\overset{−} {{a}};{b}=−\overset{−} {{b}};{d}=\overset{−} {{d}};{e}=−\overset{−} {{e}} \\ $$$$\frac{{b}−{a}}{−{b}−{a}}=\frac{{a}−{e}}{−{e}−{a}}\Rightarrow−{be}+\mathrm{2}{a}^{\mathrm{2}}…

Use-mathematical-induction-to-prove-that-the-statement-a-a-d-a-2d-a-n-1-d-n-2-2a-n-1-d-is-true-for-all-natural-numbers-Any-help-please-

Question Number 199987 by Yakubu last updated on 11/Nov/23 $$\:\boldsymbol{{Use}}\:\boldsymbol{{mathematical}}\:\boldsymbol{{induction}} \\ $$$$\:\boldsymbol{{to}}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{statement}} \\ $$$$\:\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{d}}\right)+\left(\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{d}}\right)+…+\left(\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right)=\frac{\boldsymbol{\mathrm{n}}}{\mathrm{2}}\left[\mathrm{2}\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right] \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{true}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{natural}}\:\boldsymbol{\mathrm{numbers}} \\ $$$$\boldsymbol{\mathrm{A}{ny}}\:\boldsymbol{{help}}\:\boldsymbol{{please}} \\ $$ Answered by Rasheed.Sindhi last updated…

Question-199923

Question Number 199923 by Rupesh123 last updated on 11/Nov/23 Answered by AST last updated on 11/Nov/23 $${a}+\mathrm{1}+\mathrm{1}\geqslant\mathrm{3}\sqrt[{\mathrm{3}}]{{a}}\Rightarrow\Sigma\frac{{a}}{{a}+\mathrm{2}}\leqslant\Sigma\frac{{a}^{\frac{\mathrm{2}}{\mathrm{3}}} }{\mathrm{3}} \\ $$$${Power}\:{mean}\Rightarrow\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:\geqslant\left(\frac{{a}^{\frac{\mathrm{2}}{\mathrm{3}}} +{b}^{\frac{\mathrm{2}}{\mathrm{3}}}…

find-lim-x-sin-pix-5-3x-by-sequeeze-theorem-

Question Number 199983 by cortano12 last updated on 11/Nov/23 $$\:\:\:\mathrm{find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\pi\mathrm{x}}{\mathrm{5}+\mathrm{3x}}\right)\: \\ $$$$\:\:\mathrm{by}\:\mathrm{sequeeze}\:\mathrm{theorem} \\ $$ Answered by tri26112004 last updated on 12/Nov/23 $${We}\:{have}\: \\ $$$$\mid{sin}\left(\:\frac{\pi{x}}{\mathrm{5}+\mathrm{3}{x}}\right)\mid\:\leqslant\:\mathrm{1}…

Question-199915

Question Number 199915 by lealiegalendez last updated on 11/Nov/23 Answered by Rasheed.Sindhi last updated on 11/Nov/23 $$\mathrm{5}{x}+\mathrm{30}−\mathrm{3}{x}−\mathrm{24}=\mathrm{0} \\ $$$$\mathrm{2}{x}=−\mathrm{6}\Rightarrow{x}=−\mathrm{6}/\mathrm{2}=−\mathrm{3} \\ $$ Terms of Service Privacy…

lim-x-0-2-x-3-x-5-x-3-3-x-

Question Number 199908 by cortano12 last updated on 11/Nov/23 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{2}^{\mathrm{x}} +\mathrm{3}^{\mathrm{x}} +\mathrm{5}^{\mathrm{x}} }{\mathrm{3}}\right)^{\frac{\mathrm{3}}{\mathrm{x}}} =?\: \\ $$ Answered by cortano12 last updated on 11/Nov/23 $$\:\mathrm{L}\:=\:\underset{{x}\rightarrow\mathrm{0}}…