Question Number 213518 by issac last updated on 07/Nov/24 $$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{{z}\centerdot\mathrm{sin}\left({z}\right)}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left({z}\right)}\:\mathrm{d}{z} \\ $$$$\int_{\:\mid{z}\mid=\mathrm{2}} \:\frac{\mathrm{1}}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$$$\int_{\:\mid{z}\mid=\mathrm{2}} \:\frac{\mathrm{sin}\left({z}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$ Answered by…
Question Number 213519 by RojaTaniya last updated on 07/Nov/24 Answered by mr W last updated on 07/Nov/24 $$\mathrm{tan}\:\alpha=\frac{\mathrm{1}}{{x}} \\ $$$$\mathrm{tan}\:\left(\alpha+\beta\right)=\frac{\mathrm{3}}{{x}} \\ $$$$\mathrm{tan}\:\left(\alpha+\alpha+\beta\right)=\frac{\mathrm{6}}{{x}} \\ $$$$\frac{\mathrm{6}}{{x}}=\frac{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{3}}{{x}}}{\mathrm{1}−\frac{\mathrm{1}}{{x}}×\frac{\mathrm{3}}{{x}}}=\frac{\mathrm{4}{x}}{{x}^{\mathrm{2}} −\mathrm{3}}…
Question Number 213511 by universe last updated on 07/Nov/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\:\:\left[\underset{\mathrm{r}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{r}} }\right] \\ $$$$\:\:\:\mathrm{where}\:\left[\bullet\right]\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{finction} \\ $$ Answered by issac last updated on 07/Nov/24…
Question Number 213468 by universe last updated on 06/Nov/24 $$\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{defined}\: \\ $$$$\mathrm{recurssively}\:\mathrm{by}\:\mathrm{a}_{\mathrm{1}} =\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\mathrm{a}_{\mathrm{n}\:} =\:\sqrt{\mathrm{3a}_{\mathrm{n}−\mathrm{1}\:} \:−\mathrm{2}\:}\:\:\:\:\mathrm{for}\:\mathrm{n}\geqslant\mathrm{2}\:\:\mathrm{converges}\: \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{its}\:\mathrm{limit}. \\ $$ Answered by issac…
Question Number 213503 by Spillover last updated on 06/Nov/24 Answered by mr W last updated on 06/Nov/24 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{x}^{\mathrm{2}{n}} =\frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }\:{for}\:\mid{x}\mid<\mathrm{1} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 213499 by issac last updated on 06/Nov/24 $$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{{z}\centerdot\mathrm{sin}\left({z}\right)}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left({z}\right)}\mathrm{d}{z}\:=?\:\left(\mathrm{contour}\:\mathrm{integral}\right) \\ $$$$\mathrm{pls}\:\mathrm{help}….. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 213467 by efronzo1 last updated on 06/Nov/24 $$\:\:\:\underbrace{\boldsymbol{{B}}} \\ $$ Commented by mr W last updated on 06/Nov/24 �� Commented by mr W…
Question Number 213492 by a.lgnaoui last updated on 06/Nov/24 Commented by a.lgnaoui last updated on 07/Nov/24 $$\mathrm{AH}=\mathrm{4}+\mathrm{2r}\:\:\:,\:\mathrm{6}^{\mathrm{2}} =\left(\mathrm{4}+\mathrm{r}\right)^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} \\ $$ Commented by A5T last…
Question Number 213463 by golsendro last updated on 06/Nov/24 $$\:\:\mathrm{For}\:\mathrm{p},\mathrm{q}\:\mathrm{and}\:\mathrm{r}\:\mathrm{prime}\:\mathrm{numbers}\: \\ $$$$\:\:\mathrm{satisfying}\:\begin{cases}{\mathrm{p}\left(\mathrm{q}+\mathrm{1}\right)\left(\mathrm{r}+\mathrm{1}\right)=\mathrm{1064}}\\{\mathrm{r}\left(\mathrm{p}+\mathrm{1}\right)\left(\mathrm{q}+\mathrm{1}\right)=\mathrm{1554}}\end{cases} \\ $$$$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{p}\left(\mathrm{q}+\mathrm{1}\right)\mathrm{r}\: \\ $$ Answered by A5T last updated on 06/Nov/24 $${p}\mid\mathrm{1064}=\mathrm{2}^{\mathrm{3}} ×\mathrm{7}×\mathrm{19};\:{p}+\mathrm{1}\mid\mathrm{1554}=\mathrm{2}×\mathrm{3}×\mathrm{7}×\mathrm{37}…
Question Number 213459 by golsendro last updated on 06/Nov/24 $$\:\:\mathrm{Find}\:\mathrm{tupple}\:\mathrm{natural}\:\mathrm{numbers}\:\left(\mathrm{a},\mathrm{b},\mathrm{c}\right) \\ $$$$\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\begin{cases}{\mathrm{max}\left\{\frac{\mathrm{a}+\mathrm{b}}{\mathrm{2}}+\frac{\mid\mathrm{a}−\mathrm{b}\mid}{\mathrm{2}}\:,\:\frac{\mathrm{b}+\mathrm{c}}{\mathrm{2}}+\frac{\mid\mathrm{b}−\mathrm{c}\mid}{\mathrm{2}}\:,\frac{\mathrm{c}+\mathrm{a}}{\mathrm{2}}+\frac{\mid\mathrm{c}−\mathrm{a}\mid}{\mathrm{2}}\right\}=\mathrm{a}}\\{\mathrm{min}\left\{\frac{\mathrm{a}+\mathrm{b}}{\mathrm{2}}−\frac{\mid\mathrm{a}−\mathrm{b}\mid}{\mathrm{2}}\:,\:\frac{\mathrm{b}+\mathrm{c}}{\mathrm{2}}−\frac{\mid\mathrm{b}−\mathrm{c}\mid}{\mathrm{2}}\:,\:\frac{\mathrm{c}+\mathrm{a}}{\mathrm{2}}−\frac{\mid\mathrm{c}−\mathrm{a}\mid}{\mathrm{2}}\right\}=\mathrm{b}}\end{cases} \\ $$$$\:\:\mathrm{where}\:\mathrm{a}+\mathrm{b}+\mathrm{c}\:=\:\mathrm{10} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com