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Author: Tinku Tara

sin-101x-sin-99-x-dx-

Question Number 70719 by oyemi kemewari last updated on 07/Oct/19 $$\int\mathrm{sin}\:\left(\mathrm{101x}\right)\mathrm{sin}\:^{\mathrm{99}} \mathrm{x}\:\mathrm{dx} \\ $$ Answered by mind is power last updated on 07/Oct/19 $${sin}\left(\mathrm{101}{x}\right)={sin}\left(\mathrm{100}{x}\right){cos}\left({x}\right)+{sin}\left({x}\right){cos}\left(\mathrm{100}{x}\right) \\…

Can-you-show-why-a-d-dx-sin-x-cos-x-b-d-dx-cos-x-sin-x-

Question Number 5171 by FilupSmith last updated on 25/Apr/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{show}\:\mathrm{why}: \\ $$$$\left({a}\right)\:\:\:\:\:\frac{{d}}{{dx}}\left(\mathrm{sin}\:{x}\right)=\mathrm{cos}\:{x} \\ $$$$\left({b}\right)\:\:\:\:\:\frac{{d}}{{dx}}\left(\mathrm{cos}\:{x}\right)=−\mathrm{sin}\:{x} \\ $$ Commented by FilupSmith last updated on 25/Apr/16 $${f}\:'\left({x}\right)=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}}…

lim-x-0-sinx-x-tanx-x-

Question Number 136243 by Khalmohmmad last updated on 19/Mar/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}{x}−{x}}{\mathrm{tan}{x}−{x}}=? \\ $$ Answered by EDWIN88 last updated on 20/Mar/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{x}}{\mathrm{tan}\:\mathrm{x}−\mathrm{x}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{1}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}} \\…

d-dx-log-10-x-

Question Number 70705 by sadimuhmud 136 last updated on 07/Oct/19 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{log}_{\mathrm{10}} \mathrm{x}\right)=? \\ $$ Answered by $@ty@m123 last updated on 07/Oct/19 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{log}_{{e}} \:{x}.}{\mathrm{log}_{{e}} \:\mathrm{10}}\right)=\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{10}}.\frac{{d}}{{dx}}\left(\mathrm{ln}\:{x}\right) \\…

Find-the-value-of-2023-mod-2027-

Question Number 5168 by Yozzii last updated on 24/Apr/16 $${Find}\:{the}\:{value}\:{of}\:\mathrm{2023}!\:\left({mod}\:\mathrm{2027}\right). \\ $$ Commented by prakash jain last updated on 27/Apr/16 $$\mathrm{If}\:\mathrm{you}\:\mathrm{find}\:\mathrm{an}\:\mathrm{answer},\:\mathrm{please}\:\mathrm{do}\:\mathrm{post}\:\mathrm{it}.\:\mathrm{I} \\ $$$$\mathrm{have}\:\mathrm{not}\:\mathrm{yet}\:\mathrm{been}\:\mathrm{able}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}. \\ $$…