Question Number 11843 by tawa last updated on 02/Apr/17 $$\mathrm{Differentiate},\:\:\mathrm{ln}\left(\mathrm{cosx}\right)\:\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle}. \\ $$ Answered by ajfour last updated on 02/Apr/17 $$\frac{{d}}{{dx}}\mathrm{ln}\:\left(\mathrm{cos}\:{x}\right)=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\mathrm{cos}\:\left({x}+{h}\right)−\mathrm{ln}\:\mathrm{cos}\:{x}}{{h}} \\ $$$$\:=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\:\frac{\mathrm{cos}\:\left({x}+{h}\right)}{\mathrm{cos}\:{x}}\:\right]}{{h}} \\…
Question Number 142870 by mnjuly1970 last updated on 06/Jun/21 Answered by qaz last updated on 06/Jun/21 $$\Theta=\mathrm{2}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{u}\right)\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{u}}}{\mathrm{u}}\mathrm{du} \\ $$$$=\mathrm{2}\left\{\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{u}\right)\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{u}}}{\mathrm{u}}\mathrm{du}+\int_{\mathrm{0}}…
Question Number 142854 by liberty last updated on 06/Jun/21 $$\:\:{The}\:{maximum}\:{value}\:{of}\: \\ $$$$\:{y}=\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({x}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{2}} }−\sqrt{{x}^{\mathrm{2}} +\left({x}−\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$$$\:{is}\: \\ $$ Commented by 1549442205PVT last…
Question Number 11769 by Nayon last updated on 31/Mar/17 $${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0}\:{solve} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77294 by Rabnawaz last updated on 05/Jan/20 $${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{27}{x} \\ $$$${Find}\:{intervals}\:{where}\:{given}\:{fuction}\:{ii} \\ $$$${is} \\ $$$$\mathrm{1}.{increasing} \\ $$$$\mathrm{2}.{decreasing} \\ $$$$\mathrm{3}\:{concave}\:{up}\:{and}\:{down} \\ $$$$\mathrm{4}\:{point}\:{of}\:{inflection} \\ $$…
Question Number 77271 by jagoll last updated on 05/Jan/20 $$\mathrm{given}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}.\:\mathrm{The}\:\mathrm{tangent}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{with}\:\mathrm{the}\:\mathrm{smallest}\: \\ $$$$\mathrm{gradient}\:\mathrm{is}\:.. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 142777 by alcohol last updated on 05/Jun/21 Commented by karannagar last updated on 05/Jun/21 $${yes}\:{i}\:{solve} \\ $$ Commented by alcohol last updated on…
Question Number 142773 by mnjuly1970 last updated on 05/Jun/21 $$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}\:……{integral}…… \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \frac{{li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{\mathrm{2}−{x}}\:{dx}=?? \\ $$$$\:…….{m}.{n}… \\ $$ Answered by mnjuly1970 last…
Question Number 11653 by Nayon last updated on 29/Mar/17 $${Can}\:{you}\:{give}\:{me}\:{some}\:{problem} \\ $$$${from}\:{your}\:{calculus}\:{text}\:{book}… \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 142723 by mnjuly1970 last updated on 04/Jun/21 $$\:\:\:\:\:\:\:\:…….\:{discrete}\:\:…..\:\:{mathematics}……. \\ $$$$\:\:\:\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{F}_{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1}}\overset{?} {=}\frac{\mathrm{5}−\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:{F}_{{n}} \:::\:{fibonacci}\:\:{sequence}… \\ $$ Answered by…