Question Number 134998 by snipers237 last updated on 09/Mar/21 $$\:\:\:{Let}\:\:{I}=\:\int_{\mid{z}\mid=\pi} \frac{{tan}\left(\overset{−} {{z}}\right)}{{z}−\mathrm{4}}\:{dz}\:\: \\ $$$$\:{J}=\int_{\mid{z}\mid=\pi} \frac{{cos}\left(\overset{−} {{z}}\right)}{{z}−\mathrm{4}}\:{dz}\:\:\:{and}\:\:{K}=\int_{\mid{z}\mid=\pi} \frac{{cos}\left({Re}\left({z}\right)\right){cos}\left({Im}\left({z}\right)\right)}{{z}−\mathrm{4}}{dz} \\ $$$$\:{Show}\:{that}\:\:{I}={J}\sqrt{\mathrm{2}}=−{i}\pi \\ $$$$\:{Show}\:{that}\:\:{J}={K} \\ $$ Terms of…
Question Number 69457 by mhmd last updated on 23/Sep/19 $${find}\:{value}\:{log}\mathrm{40}/\mathrm{9}\:\:+\mathrm{4}{log}\mathrm{5}\:\:+\mathrm{2}{log}\mathrm{6}\:\:? \\ $$ Answered by MJS last updated on 23/Sep/19 $$\mathrm{log}\:\frac{\mathrm{40}}{\mathrm{9}}\:+\mathrm{4log}\:\mathrm{5}\:+\mathrm{2log}\:\mathrm{6}\:= \\ $$$$=\mathrm{log}\:\mathrm{40}\:−\mathrm{log}\:\mathrm{9}\:+\mathrm{4log}\:\mathrm{5}\:+\mathrm{2log}\:\mathrm{2}\:+\mathrm{2log}\:\mathrm{3}= \\ $$$$=\mathrm{3log}\:\mathrm{2}\:+\mathrm{log}\:\mathrm{5}\:−\mathrm{2log}\:\mathrm{3}\:+\mathrm{4log}\:\mathrm{5}\:+\mathrm{2log}\:\mathrm{2}\:+\mathrm{2log}\:\mathrm{3}= \\…
Question Number 69355 by cesar.marval.larez@gmail.com last updated on 22/Sep/19 $$ \\ $$$${Find}\:{the}\:{maximun}\:{and}\:{minimum}\: \\ $$$${values}\:{of}\:{the}\:{function}\:{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{7} \\ $$$${and}\:{sketch}\:{its}\:{graph}\: \\ $$ Answered by MJS last updated on…
Question Number 134878 by bemath last updated on 08/Mar/21 Answered by EDWIN88 last updated on 08/Mar/21 $$\mathrm{B}\left(\theta\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}.\mathrm{100}.\mathrm{sin}\:\theta\:=\:\mathrm{50}\:\mathrm{sin}\:\theta\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{radius}\:\mathrm{of}\:\mathrm{semi}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{r}\:=\:\mathrm{10}.\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right) \\ $$$$\mathrm{so}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{semi}\:\mathrm{circle}\:\mathrm{A}\left(\theta\right)=\frac{\mathrm{1}}{\mathrm{2}}\pi\left(\mathrm{100}.\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right)\right) \\ $$$$\mathrm{A}\left(\theta\right)\:=\:\mathrm{50}\pi\:\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right)…
Question Number 134874 by bemath last updated on 08/Mar/21 $$\mathrm{The}\:\mathrm{two}\:\mathrm{side}\:\mathrm{of}\:\mathrm{rectangle}\:\mathrm{are} \\ $$$$\mathrm{2}{x}\:\mathrm{and}\:\left(!\mathrm{5}−\mathrm{2}{x}\right)\:\mathrm{units}\:\mathrm{respectively} \\ $$$$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{rectangle}\:\mathrm{will}\:\mathrm{be}\:\mathrm{maximum}? \\ $$ Commented by Ñï= last updated on 08/Mar/21…
Question Number 134871 by Raxreedoroid last updated on 08/Mar/21 $$\mathrm{What}\:\mathrm{is}\:{f}\left({x}\right)? \\ $$$$\mathrm{such}\:\mathrm{that}\:\left({f}\left({x}\right)+{f}\:'\left({x}\right)\mathrm{ln}\:{x}\right)\mathrm{ln}\:{x}=−\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134852 by mnjuly1970 last updated on 07/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:{find}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}{dx}=? \\ $$$$ \\ $$ Answered by mnjuly1970 last updated…
Question Number 134843 by Raxreedoroid last updated on 07/Mar/21 $$\mathrm{what}\:\mathrm{is}\:{f}\left({x}\right)? \\ $$$$\mathrm{such}\:\mathrm{that}\:\frac{{f}\left({x}\right)}{{x}}+{f}\:'\left({x}\right)\mathrm{ln}\:{x}=\mathrm{0} \\ $$ Commented by PRITHWISH SEN 2 last updated on 07/Mar/21 $$\frac{\mathrm{C}}{\mathrm{lnx}}\:\:\left(\mathrm{C}=\:\mathrm{constant}\right) \\…
Question Number 134809 by liberty last updated on 07/Mar/21 $${Show}\:{if}\:{f}\:''\left({a}\right)\:{exist}\:{then}\: \\ $$$${f}\:''\left({a}\right)=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({a}+{h}\right)+{f}\left({a}−{h}\right)−\mathrm{2}{f}\left({a}\right)}{{h}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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}} \\…