Question Number 3707 by Filup last updated on 19/Dec/15 $$\mathrm{lets}\:\mathrm{say}\:\mathrm{we}\:\mathrm{have}\:\mathrm{a}\:\mathrm{function}\:{f}\left({x}\right). \\ $$$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{at}\:{x}={n}\:\mathrm{makes}\:\mathrm{an} \\ $$$$\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:{x}−\mathrm{axis}. \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle} \\ $$$$\mathrm{as}\:\mathrm{we}\:\mathrm{change}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}? \\ $$$$ \\ $$$$\mathrm{Suppose}\:{f}\left({x}\right)={x}^{\mathrm{2}} \\…
Question Number 69243 by Kunal12588 last updated on 21/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69241 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $$\:{Let}\:{consider}\:{K}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\left(\mathrm{1}−{x}^{{a}} \right)\left(\mathrm{1}−{x}^{{b}} \right)\left(\mathrm{1}−{x}^{{c}} \right)}{\left({x}−\mathrm{1}\right){lnx}}{dx}\: \\ $$$${prove}\:{that}\: \\ $$$${e}^{{K}} =\:\frac{\left({a}+{b}\right)!\left({a}+{c}\right)!\left({b}+{c}\right)!}{{a}!{b}!{c}!\left({a}+{b}+{c}\right)!}\:\:…
Question Number 69238 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $${Use}\:{Residus}\:{Theorem}\:{to}\:{explicit}\: \\ $$$${f}\left({a}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}} {sin}\left({na}\right)}{{n}^{\mathrm{3}} }\:\: \\ $$ Commented by…
Question Number 134772 by bramlexs22 last updated on 07/Mar/21 $$ \\ $$What is the equation of a circle that goes through points (0,1), (1,4), and…
Question Number 69236 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $${Use}\:\:{Residus}\:{theorem}\:{to}\:{prove}\:{that}\:\forall\:{a}>\mathrm{0}\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:{n}^{\mathrm{2}} +{a}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\pi}{{ash}\left(\pi{a}\right)}\:\:\:−\frac{\mathrm{1}}{{a}^{\mathrm{2}} }\right) \\ $$$${and}\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}}…
Question Number 134769 by abdurehime last updated on 07/Mar/21 Commented by abdurehime last updated on 07/Mar/21 $$\mathrm{please}\:\mathrm{be}?\mathrm{fast} \\ $$ Commented by john_santu last updated on…
Question Number 134768 by abdurehime last updated on 07/Mar/21 Commented by abdurehime last updated on 07/Mar/21 $$\mathrm{be}\:\mathrm{fast}\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{in}\:\mathrm{10}\:\mathrm{min} \\ $$ Commented by mr W last updated…
Question Number 134770 by abdurehime last updated on 07/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69233 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $${Prove}\:{that}\:\:{B}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\left[{ln}\left(−{lnu}\right)\right]^{\mathrm{2}} \:{du}\:=\:\gamma^{\mathrm{2}} +\:\zeta\left(\mathrm{2}\right)\:\: \\ $$ Commented by mathmax by…