Question Number 115534 by Hassen_Timol last updated on 26/Sep/20 $$\mathrm{Let}\:\mathrm{say}\:{r}^{\left({n}\right)} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({r}−{k}\right)\:\mathrm{and}\:{r}^{\left(\mathrm{0}\right)} =\mathrm{1} \\ $$$$\mathrm{With}\:{n}\in\mathbb{N}\:\mathrm{and}\:{r}\in\mathbb{R}… \\ $$$$\mathrm{1}.\:\:\:\mathrm{Show}\:\mathrm{that}\:\left({n}−\mathrm{1}−{r}\right)^{\left({n}\right)} \:=\:\left(−\mathrm{1}\right)^{\left({n}\right)} \left({r}\right)^{\left({n}\right)} \\ $$$$\mathrm{2}.\:\mathrm{If}\:{m}\leqslant{n},\:\mathrm{show}\:\mathrm{that}\:\:\frac{{r}^{\left({n}\right)} }{{r}^{\left({m}\right)} }=\left({r}−{m}\right)^{\left({n}−{m}\right)} \\…
Question Number 181062 by 123564 last updated on 21/Nov/22 $${Q}\mathrm{180886} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115498 by bobhans last updated on 26/Sep/20 $$\int\:\mathrm{sec}\:{x}\:{dx}\:? \\ $$$$\int\:\sqrt{{x}−\sqrt{{x}}}\:{dx}\:? \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\sqrt[{{n}\:}]{\mathrm{1}+\sqrt{\mathrm{1}+{n}^{\mathrm{2}} }}\right)\left(\sqrt[{{n}\:}]{\mathrm{2}+\sqrt{\mathrm{4}+{n}^{\mathrm{2}} }}\right)\left(\sqrt[{{n}\:}]{\mathrm{3}+\sqrt{\mathrm{9}+{n}^{\mathrm{2}} }}\right)…\left(\sqrt[{{n}\:}]{{n}+\sqrt{\mathrm{2}{n}^{\mathrm{2}} }}\right)}{{n}}? \\ $$ Commented by bobhans last…
Question Number 115499 by mathdave last updated on 26/Sep/20 $${form}\:{a}\:{double}\:{integral}\:{to}\:{represent} \\ $$$${the}\:{area}\:{of}\:{a}\:{plane}\:{fiqure}\:{bounded}\:{by} \\ $$$${the}\:{polar}\:{centre} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115472 by Khalmohmmad last updated on 26/Sep/20 Commented by malwaan last updated on 26/Sep/20 $${x}\rightarrow−\infty \\ $$$$\mid{x}−\mathrm{2}\mid=−{x}+\mathrm{2} \\ $$$$\mid{x}+\mathrm{1}\mid=−{x}−\mathrm{1} \\ $$$$\therefore\:\underset{{x}\rightarrow−\infty} {{lim}}\:\frac{\mathrm{3}{x}−{x}+\mathrm{2}}{\mathrm{5}{x}+{x}+\mathrm{1}}\: \\…
Question Number 115471 by manuel2456 last updated on 26/Sep/20 $${For}\:{angles}\:{a},{b},{c}\in\mathbb{R}\:{with}\:{a}+{b}+{c}=\pi,\: \\ $$$${prove}\:{the}\:{following}\:{identities}: \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{{a}}{\mathrm{2}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{b}}{\mathrm{2}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{c}}{\mathrm{2}}\right)=\left(\mathrm{tan}\left(\frac{{a}}{\mathrm{2}}\right)\mathrm{tan}\left(\frac{{b}}{\mathrm{2}}\right)\mathrm{tan}\left(\frac{{c}}{\mathrm{2}}\right)\right)^{−\mathrm{1}} \\ $$$$\mathrm{H}{elp} \\ $$$$ \\ $$ Commented by…
Question Number 115438 by A8;15: last updated on 25/Sep/20 Answered by Olaf last updated on 26/Sep/20 $${the}\:{function}\:{is}\:{odd} \\ $$$${and}\:{the}\:{domain}\:{is}\:{symmetrical} \\ $$$${so}\:{the}\:{result}\:{is}\:\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{Sorry}}\:\boldsymbol{\mathrm{I}}'\boldsymbol{\mathrm{m}}\:\boldsymbol{\mathrm{wrong}}. \\ $$$$\boldsymbol{\mathrm{see}}\:\boldsymbol{\mathrm{mister}}\:\boldsymbol{\mathrm{abdo}}.…
Question Number 115439 by Hassen_Timol last updated on 25/Sep/20 Commented by Hassen_Timol last updated on 26/Sep/20 How can I solve it please....? Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 180974 by yaslm last updated on 19/Nov/22 Commented by mr W last updated on 19/Nov/22 $${ask}\:{such}\:{questions}\:{best}\:{in}\:{google} \\ $$ Terms of Service Privacy Policy…
Question Number 115418 by mohammad17 last updated on 25/Sep/20 Commented by mohammad17 last updated on 25/Sep/20 $${help}\:{me}\:{sir}\:{i}\:{want}\:\left({H}.{W}\right) \\ $$ Answered by Dwaipayan Shikari last updated…