Question Number 61210 by pooja24 last updated on 30/May/19 $${for}\:{what}\:{value}\:{of}\:\theta,\:\:{e}^{{i}\theta} =\mathrm{0}\:\: \\ $$ Commented by Tony Lin last updated on 30/May/19 $${e}^{{i}\theta} ={cos}\theta+{isin}\theta \\ $$$$\:\:\:\:\:{cos}\theta\in\left[−\mathrm{1},\mathrm{1}\right]\in{R}…
Question Number 126704 by Dwaipayan Shikari last updated on 23/Dec/20 $$\frac{{e}^{\pi} −\mathrm{1}}{{e}^{\pi} +\mathrm{1}}=\frac{\pi}{\mathrm{2}+\frac{\pi^{\mathrm{2}} }{\mathrm{6}+\frac{\pi^{\mathrm{2}} }{\mathrm{10}+\frac{\pi^{\mathrm{2}} }{\mathrm{14}+….}}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61165 by Tawa1 last updated on 29/May/19 Answered by MJS last updated on 30/May/19 $$\int\frac{\mathrm{cos}^{\mathrm{2}} \:\left(\mathrm{2}{x}−\mathrm{5}\right)\:\mathrm{cos}\:\left(\mathrm{2}{x}−\mathrm{14}\right)}{\mathrm{cos}\:\left(\mathrm{2}{x}−\mathrm{7}\right)}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2}{x}−\mathrm{7}\:\rightarrow\:{dx}=\frac{{dt}}{\mathrm{2}}\right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{cos}^{\mathrm{2}} \:\left({t}+\mathrm{2}\right)\:\mathrm{cos}\:\left({t}−\mathrm{7}\right)}{\mathrm{cos}\:\left({t}\right)}{dt}= \\ $$$$\:\:\:\:\:\left[\mathrm{use}\:\mathrm{these}:\right.…
Question Number 192238 by Kallu last updated on 12/May/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61147 by malwaan last updated on 29/May/19 $$\boldsymbol{{prove}} \\ $$$$\int\frac{\mathrm{1}+{cos}\:{x}}{\mathrm{1}−{cos}\:{x}}{dx}=−\mathrm{2}{cot}\:\frac{{x}}{\mathrm{2}}−{x}+{c} \\ $$$$ \\ $$ Answered by tanmay last updated on 29/May/19 $$\int\frac{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 126669 by Dwaipayan Shikari last updated on 23/Dec/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} ^{\mathrm{2}} }{{n}^{\mathrm{4}} } \\ $$ Commented by talminator2856791 last updated on 23/Dec/20…
Question Number 126632 by BHOOPENDRA last updated on 22/Dec/20 Commented by BHOOPENDRA last updated on 22/Dec/20 $${thanku}\:{sir} \\ $$ Answered by Ar Brandon last updated…
Question Number 192160 by universe last updated on 10/May/23 $$\mathrm{if}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\mathrm{are}\:\mathrm{three}\:\mathrm{distinct}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{x}}{\mathrm{y}−{z}}+\frac{\mathrm{y}}{\mathrm{z}−\mathrm{x}}+\frac{\mathrm{z}}{\mathrm{x}−\mathrm{y}}\:=\:\mathrm{0}\:\mathrm{then}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\Sigma\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{y}−\mathrm{z}\right)^{\mathrm{2}} } \\ $$ Commented by mehdee42 last updated on 09/May/23…
Question Number 192138 by Mastermind last updated on 09/May/23 $$\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\left\{_{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)=\left(\mathrm{0},\mathrm{0}\right)} ^{\frac{\mathrm{x}^{\mathrm{2}} \mathrm{y}}{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{2y}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)\neq\:\left(\mathrm{0},\mathrm{0}\right)} \right. \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{directional}\:\mathrm{derivative}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{direction}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arbitrary}\:\mathrm{unit}\:\mathrm{vector} \\ $$$$\phi\:\mathrm{at}\:\left(\mathrm{0},\mathrm{0}\right),\:\mathrm{but}\:\mathrm{f}\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{continous}\:\mathrm{at}\:\left(\mathrm{0},\mathrm{0}\right)\: \\ $$…
Question Number 192129 by universe last updated on 08/May/23 $$\:{prove}\:{that} \\ $$$$\:\mid{a}+\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }\mid\:+\:\mid{a}\:−\:\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }\mid\:=\:\mid{a}+{b}\mid\:+\mid{a}−{b}\mid \\ $$$${a},{b}\:\in\:\mathbb{C} \\ $$ Answered by AST last updated…