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Category: Differentiation

Let-I-z-pi-tan-z-z-4-dz-J-z-pi-cos-z-z-4-dz-and-K-z-pi-cos-Re-z-cos-Im-z-z-4-dz-Show-that-I-J-2-ipi-Show-that-J-K-

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…

find-value-log40-9-4log5-2log6-

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-134878

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)…

The-two-side-of-rectangle-are-2x-and-5-2x-units-respectively-For-what-value-of-x-the-area-of-rectangle-will-be-maximum-

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…

nice-calculus-find-0-1-ln-x-ln-1-x-x-1-x-dx-

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…

lets-say-we-have-a-function-f-x-The-tangent-line-at-x-n-makes-an-angle-with-the-x-axis-What-is-the-rate-of-change-of-the-angle-as-we-change-the-value-of-x-Suppose-f-x-x-2-

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}} \\…