Question Number 117863 by aurpeyz last updated on 14/Oct/20 $${if}\:{y}=\frac{{x}+\mathrm{2}}{\:\sqrt{{x}+\mathrm{1}}}\:{find}\:\frac{{dy}}{{dx}}\:{from}\:{first} \\ $$$${principle}. \\ $$ Answered by bemath last updated on 14/Oct/20 $$\mathrm{y}=\frac{\mathrm{x}+\mathrm{1}+\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}}\:=\:\sqrt{\mathrm{x}+\mathrm{1}}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{h}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{h}+\mathrm{1}}}−\sqrt{\mathrm{x}+\mathrm{1}}\:−\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}}}{\mathrm{h}}…
Question Number 117800 by Khalmohmmad last updated on 13/Oct/20 Answered by mr W last updated on 13/Oct/20 $$\mathrm{log}\:\mathrm{2}=\mathrm{log}\:\frac{\mathrm{6}}{\mathrm{3}}=\mathrm{log}\:\mathrm{6}−\mathrm{log}\:\mathrm{3}={a}−{b} \\ $$$$\mathrm{log}\:\mathrm{25}=\mathrm{log}\:\left(\frac{\mathrm{10}}{\mathrm{2}}\right)^{\mathrm{2}} =\mathrm{2}\left(\mathrm{log}\:\mathrm{10}−\mathrm{log}\:\mathrm{2}\right) \\ $$$$=\mathrm{2}\left(\mathrm{1}−{a}+{b}\right) \\ $$…
Question Number 183330 by Matica last updated on 25/Dec/22 $$\:\:{S}\:=\:{sinhx}+{sinh}^{\mathrm{2}} {x}\:+\:{sinh}^{\mathrm{3}} {x}+…+{sinh}^{{n}} {x}=? \\ $$ Commented by mokys last updated on 25/Dec/22 $${S}\:=\:\frac{{sinhx}}{\mathrm{1}−{sinhx}} \\ $$…
Question Number 52258 by hassentimol last updated on 05/Jan/19 Commented by hassentimol last updated on 05/Jan/19 $$\mathrm{How}\:\mathrm{can}\:\mathrm{I}\:\mathrm{prove}\:\mathrm{that}\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 117791 by ZiYangLee last updated on 13/Oct/20 $$\mathrm{If}\:{k}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{which}\:\mathrm{satisfies}\: \\ $$$$\mathrm{2sin}^{\mathrm{2}} \theta+\mathrm{10cos}^{\mathrm{2}} \frac{\theta}{\mathrm{2}}=\mathrm{7}−\mathrm{2}{k},\:\mathrm{then}\:{k}\in? \\ $$$${A}.\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\right\}\:\:\:{B}.\left\{−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\right\} \\ $$$${C}.\left\{\left(−\mathrm{2},−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\right\}\:\:{D}.\left\{−\mathrm{3},−\mathrm{2},−\mathrm{1},\mathrm{0}\right\}\right. \\ $$ Answered by floor(10²Eta[1]) last updated…
Question Number 117787 by mathdave last updated on 13/Oct/20 Answered by Dwaipayan Shikari last updated on 13/Oct/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \frac{\mathrm{1}−{x}^{{n}} }{\mathrm{1}−{x}}{dx} \\ $$$$=\underset{{n}\rightarrow\infty}…
Question Number 183301 by sciencestudent last updated on 24/Dec/22 $$\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{249}}\end{pmatrix}+\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{250}}\end{pmatrix}=? \\ $$ Commented by JDamian last updated on 24/Dec/22 https://en.m.wikipedia.org/wiki/Pascal%27s_triangle Commented by sciencestudent last updated…
Question Number 183270 by Ml last updated on 24/Dec/22 Commented by Ml last updated on 24/Dec/22 $$\mathrm{Area}\:\mathrm{and}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{sheadd} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{have}\:\mathrm{exam}\: \\ $$$$\mathrm{i}\:\mathrm{need}\:\mathrm{it} \\ $$ Commented by…
Question Number 183247 by SANOGO last updated on 24/Dec/22 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cos}\left({t}\right){ln}\left({tant}\right){dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 52161 by naka3546 last updated on 03/Jan/19 Commented by prakash jain last updated on 04/Jan/19 $${f}\left({x}\right)=\begin{cases}{\mathrm{7}{x}+\mathrm{1}}&{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}/\mathrm{2}}\\{\mathrm{7}−\mathrm{5}{x}}&{\mathrm{1}/\mathrm{2}\leqslant{x}\leqslant\mathrm{1}}\end{cases} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{2}} {f}\left({x}\right){dx}+\int_{\mathrm{1}\:/\mathrm{2}} ^{\mathrm{1}}…