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Question-72251

Question Number 72251 by aliesam last updated on 26/Oct/19 Commented by mathmax by abdo last updated on 26/Oct/19 $${let}\:{f}\left({x}\right)=\frac{{ln}\left(\mathrm{1}+{ax}+{bx}^{\mathrm{2}} \right)−{ln}\left(\mathrm{1}−{ax}+{bx}^{\mathrm{2}} \right)}{\mathrm{1}−{cosx}} \\ $$$${we}\:{have}\:{ln}^{'} \left(\mathrm{1}+{u}\right)=\frac{\mathrm{1}}{\mathrm{1}+{u}}\:=\mathrm{1}−{u}\:+{o}\left({u}\right)\:\left({u}\rightarrow\mathrm{0}\right)\:\Rightarrow \\…

A-string-AB-of-lenght-2l-has-a-particle-attached-to-its-midpoint-C-The-ends-A-and-B-of-the-string-are-fastened-to-two-fixed-points-with-A-distance-l-vertically-above-B-With-both-parts-of-the-string-

Question Number 137787 by physicstutes last updated on 06/Apr/21 $$\mathrm{A}\:\mathrm{string}\:{AB}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{2}{l}\:\mathrm{has}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{its}\:\mathrm{midpoint}\:\mathrm{C}.\: \\ $$$$\mathrm{The}\:\mathrm{ends}\:{A}\:\mathrm{and}\:{B}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}\:\mathrm{are}\:\mathrm{fastened}\:\mathrm{to}\:\mathrm{two}\:\mathrm{fixed}\:\mathrm{points} \\ $$$$\mathrm{with}\:{A}\:\mathrm{distance}\:{l}\:\mathrm{vertically}\:\mathrm{above}\:\mathrm{B}.\mathrm{With}\:\mathrm{both}\:\mathrm{parts}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string} \\ $$$$\mathrm{taunt},\mathrm{the}\:\mathrm{particle}\:\mathrm{describes}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{about}\:\mathrm{the}\:\mathrm{line}\:{AB}\:\mathrm{with} \\ $$$$\mathrm{constant}\:\mathrm{angular}\:\mathrm{speed}\:\omega.\:\mathrm{If}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{in}\:{CA}\:\mathrm{is}\:\mathrm{three}\:\mathrm{times} \\ $$$$\mathrm{that}\:\mathrm{in}\:{CB},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{angular}\:\mathrm{velocity}\:\mathrm{is}\:\mathrm{2}\sqrt{\frac{\mathrm{g}}{{l}}}\:. \\ $$ Answered by mr…

Question-72247

Question Number 72247 by TawaTawa last updated on 26/Oct/19 Answered by mind is power last updated on 26/Oct/19 $$\mathrm{s}_{\mathrm{1}} =\mathrm{s}_{\mathrm{2}} =\mathrm{s} \\ $$$$\frac{\mathrm{TS}}{\mathrm{PR}}=\frac{\mathrm{QT}}{\mathrm{QP}}\Rightarrow\mathrm{TS}=\frac{\mathrm{41}}{\mathrm{3}} \\ $$$$\mathrm{a}=\angle\mathrm{QST}\:,\mathrm{r}=\angle\mathrm{QST}=\angle\mathrm{PRQ}…

dx-sinx-sin2x-dx-

Question Number 6710 by Tawakalitu. last updated on 15/Jul/16 $$\int\:\frac{{dx}}{{sinx}\:+\:{sin}\mathrm{2}{x}}\:{dx} \\ $$ Answered by Yozzii last updated on 15/Jul/16 $${I}=\int\frac{{dx}}{{sinx}+{sin}\mathrm{2}{x}}=\int\frac{{sinx}}{{sin}^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{2}{cosx}\right)}{dx} \\ $$$${I}=\int\frac{−{sinx}}{−\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right)\left(\mathrm{1}+\mathrm{2}{cosx}\right)}{dx} \\…

Some-birds-were-flying-and-met-a-bird-the-bird-greeted-them-and-said-how-are-you-hundred-The-birds-said-we-are-not-hundred-we-need-half-of-us-plus-you-to-make-hundred-How-many-birds-were-flying-

Question Number 137783 by otchereabdullai@gmail.com last updated on 06/Apr/21 $$\mathrm{Some}\:\mathrm{birds}\:\mathrm{were}\:\mathrm{flying}\:\mathrm{and}\:\mathrm{met}\:\mathrm{a}\: \\ $$$$\mathrm{bird},\:\mathrm{the}\:\mathrm{bird}\:\mathrm{greeted}\:\mathrm{them}\:\mathrm{and}\:\mathrm{said} \\ $$$$\mathrm{how}\:\mathrm{are}\:\mathrm{you}\:\mathrm{hundred}.\:\mathrm{The}\:\mathrm{birds}\:\mathrm{said} \\ $$$$\mathrm{we}\:\mathrm{are}\:\mathrm{not}\:\mathrm{hundred},\:\mathrm{we}\:\mathrm{need}\:\mathrm{half}\:\mathrm{of}\:\mathrm{us} \\ $$$$\mathrm{plus}\:\mathrm{you}\:\mathrm{to}\:\mathrm{make}\:\mathrm{hundred}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{birds}\:\mathrm{were}\:\mathrm{flying} \\ $$ Answered by physicstutes…

lim-x-0-cos-px-cos-qx-x-2-

Question Number 137773 by Ajadiazeemolamilekan last updated on 06/Apr/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{px}−\mathrm{cos}\:{qx}}{{x}^{\mathrm{2}} } \\ $$ Answered by bemath last updated on 06/Apr/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\mathrm{2sin}\:\left(\frac{{p}+{q}}{\mathrm{2}}\:{x}\right)\mathrm{sin}\:\left(\frac{{p}−{q}}{\mathrm{2}}\:{x}\right)}{{x}^{\mathrm{2}} } \\…

l-x-0-im-x-sin-x-x-2-e-x-1-

Question Number 6703 by love math last updated on 15/Jul/16 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{l}im}\frac{{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} \left({e}^{{x}} −\mathrm{1}\right)} \\ $$ Answered by FilupSmith last updated on 15/Jul/16 $${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}}…