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Author: Tinku Tara

f-x-2-0-x-2t-f-t-2-dt-then-1-2-f-x-dx-

Question Number 193768 by cortano12 last updated on 19/Jun/23 $$\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2}+\underset{\mathrm{0}} {\overset{\:\mathrm{x}} {\int}}\left(\mathrm{2t}+\mathrm{f}\left(\mathrm{t}\right)\right)^{\mathrm{2}} \mathrm{dt}\: \\ $$$$\:\:\mathrm{then}\:\underset{−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:= \\ $$ Answered by gatocomcirrose last updated on…

prove-that-1-2-3-4-5-6-7-8-9-10-99-100-gt-1-13-

Question Number 193760 by York12 last updated on 19/Jun/23 $${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{7}}{\mathrm{8}}×\frac{\mathrm{9}}{\mathrm{10}}…×\frac{\mathrm{99}}{\mathrm{100}}>\frac{\mathrm{1}}{\mathrm{13}}\:\:\: \\ $$ Answered by MM42 last updated on 19/Jun/23 $${can}\:{br}\:{show}\::\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\:\frac{\mathrm{2}{i}−\mathrm{1}}{\mathrm{2}{i}}\:>\:\frac{\mathrm{11}}{\mathrm{10}\sqrt{\mathrm{4}{n}+\mathrm{1}}} \\…

Question-193726

Question Number 193726 by mr W last updated on 18/Jun/23 Answered by som(math1967) last updated on 18/Jun/23 $${a}+{b}+{c} \\ $$$$=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}\:+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}+\mathrm{tan}^{−\mathrm{1}} \mathrm{1} \\ $$$$=\mathrm{tan}^{−\mathrm{1}}…

prove-that-a-log-a-N-N-

Question Number 193721 by sciencestudentW last updated on 18/Jun/23 $${prove}\:{that}\:{a}^{{log}_{{a}} {N}} ={N} \\ $$ Answered by MATHEMATICSAM last updated on 18/Jun/23 $$\mathrm{From}\:\mathrm{log}\:\mathrm{definition}\:\mathrm{we}\:\mathrm{know}\:\mathrm{if} \\ $$$${a}^{{x}} \:=\:{N}\:\mathrm{then}\:\mathrm{we}\:\mathrm{can}\:\mathrm{write}\:\mathrm{it}\:\mathrm{as}…

Ques-3-Show-that-Z-4-is-a-group-Hence-find-the-order-of-the-group-and-of-the-element-2-Z-4-if-it-exists-Ques-4-Prove-the-if-a-b-are-any-elements-of-a-group-G-then-the-e

Question Number 193712 by Mastermind last updated on 18/Jun/23 $$\mathrm{Ques}.\:\mathrm{3}\: \\ $$$$\:\:\:\:\:\mathrm{Show}\:\mathrm{that}\:\left(\mathbb{Z}_{\mathrm{4}} ,\:+\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{group}.\:\mathrm{Hence} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{the}\:\mathrm{group}\:\mathrm{and}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{element}\:\mathrm{2}\in\mathbb{Z}_{\mathrm{4}} ,\:\mathrm{if}\:\mathrm{it}\:\mathrm{exists}. \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{4} \\ $$$$\:\:\:\:\:\mathrm{Prove}\:\mathrm{the}\:\mathrm{if}\:\mathrm{a},\mathrm{b}\:\mathrm{are}\:\mathrm{any}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{a}\: \\…