Question Number 155421 by SANOGO last updated on 30/Sep/21 Answered by puissant last updated on 30/Sep/21 $${Q}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sint}}{\mathrm{1}+{cos}^{\mathrm{2}} {t}}{dt}\:=\:−\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{−{sint}}{\mathrm{1}+{cos}^{\mathrm{2}} {t}}{dt} \\ $$$$=−\left[{arctan}\left({cost}\right)\right]_{\mathrm{0}}…
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Question Number 155420 by amin96 last updated on 30/Sep/21 $$\frac{\mathrm{1}}{\mathrm{42}}+\frac{\mathrm{1}}{\mathrm{72}}+\frac{\mathrm{1}}{\mathrm{110}}+\ldots=? \\ $$ Answered by puissant last updated on 01/Oct/21 $${S}=\frac{\mathrm{1}}{\mathrm{42}}+\frac{\mathrm{1}}{\mathrm{72}}+\frac{\mathrm{1}}{\mathrm{110}}+…….=\frac{\mathrm{1}}{\mathrm{6}}−\frac{\mathrm{1}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{9}}+…. \\ $$$$\Rightarrow\:{S}=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{2}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)}=\frac{\mathrm{1}}{\mathrm{4}}\underset{{n}=\mathrm{2}} {\overset{\infty}…
Question Number 89882 by student work last updated on 19/Apr/20 Answered by Joel578 last updated on 19/Apr/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}!\left(\mathrm{1}−\:{x}\:−\:\mathrm{1}\right)}{\left(\mathrm{2}{x}−\mathrm{1}\right){x}!}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{−{x}}{\mathrm{2}{x}−\mathrm{1}}\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by TANMAY…
Question Number 24347 by math solver last updated on 16/Nov/17 Commented by math solver last updated on 16/Nov/17 $$\mathrm{it}\:\mathrm{have}\:\:\mathrm{more}\:\mathrm{than}\:\mathrm{1}\:\mathrm{answer}. \\ $$ Commented by math solver…
Question Number 89878 by malwaan last updated on 19/Apr/20 $$\boldsymbol{{A}}\:\boldsymbol{{four\_digit}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{is}}\:\boldsymbol{{interesting}}\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}}\:\boldsymbol{{leftmost}}\:\boldsymbol{{two}} \\ $$$$\boldsymbol{{digits}}\:\boldsymbol{{is}}\:\boldsymbol{{twice}}\:\boldsymbol{{as}}\:\boldsymbol{{large}}\:\boldsymbol{{as}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{number}}\:\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{rightmost}}\:\boldsymbol{{two}}\:\boldsymbol{{digits}}. \\ $$$$\left(\boldsymbol{{for}}\:\boldsymbol{{example}}\:\mathrm{2010}\:\boldsymbol{{is}}\:\boldsymbol{{interesting}}\right) \\ $$$$\mathrm{1}\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{largest}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\…
Question Number 89874 by M±th+et£s last updated on 19/Apr/20 $$\int_{\frac{\mathrm{1}}{\mathrm{3}}} ^{\frac{\mathrm{2}}{\mathrm{3}}} \:\frac{{ln}\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{3}}}\right)}{{x}\sqrt{{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{3}}}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 24332 by Zezo9970010@gmail.com last updated on 15/Nov/17 $$\mathrm{z}^{−\mathrm{4}_{=\mathrm{1}/\mathrm{3}\left(\mathrm{1}−\sqrt{\left.\mathrm{3i}\right)}\right.} } ? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155400 by TVTA last updated on 30/Sep/21 $${x}^{\mathrm{2}} +{x}+\mathrm{5}{xy}+\mathrm{6}{y}^{\mathrm{2}} +\mathrm{2}{y}−\mathrm{2}=\mathrm{0} \\ $$ Commented by MJS_new last updated on 30/Sep/21 $$\mathrm{hyperbola}\:\mathrm{with}\:\mathrm{center}\:\begin{bmatrix}{\mathrm{2}}\\{−\mathrm{1}}\end{bmatrix}\:\mathrm{and}\:\mathrm{axes} \\ $$$${a}=\mathrm{2}\sqrt{−\mathrm{7}+\mathrm{5}\sqrt{\mathrm{2}}} \\…
Question Number 89867 by M±th+et£s last updated on 19/Apr/20 $${find}\:{the}\:{integration} \\ $$$$\int{ln}\lfloor{x}\rfloor\:{dx}\:\:\:\:\:\:;\:{x}>\mathrm{2} \\ $$ Commented by ~blr237~ last updated on 20/Apr/20 Answered by mr W…