Menu Close

Category: Differentiation

Give-the-exponentional-form-of-the-complex-Z-1-cos-itan-1-cos-isin-

Question Number 75509 by ~blr237~ last updated on 12/Dec/19 $$\mathrm{Give}\:\mathrm{the}\:\mathrm{exponentional}\:\mathrm{form}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{complex}\:\mathrm{Z}=\frac{\mathrm{1}−\mathrm{cos}\theta+\mathrm{itan}\theta}{\mathrm{1}+\mathrm{cos}\theta−\mathrm{isin}\theta} \\ $$ Answered by MJS last updated on 12/Dec/19 $$\frac{\mathrm{1}−{c}+\mathrm{i}{t}}{\mathrm{1}+{c}−\mathrm{i}{s}}=\frac{{c}^{\mathrm{2}} −\mathrm{2}{c}−{st}+\mathrm{1}}{{c}^{\mathrm{2}} −\mathrm{2}{c}+{s}^{\mathrm{2}} +\mathrm{1}}−\frac{{cs}+{ct}−{s}−{t}}{{c}^{\mathrm{2}}…

Question-75463

Question Number 75463 by indalecioneves last updated on 11/Dec/19 Answered by mr W last updated on 12/Dec/19 $${shape}\:{of}\:{cable}\:{is}\:{catenary}: \\ $$$$\frac{{L}}{{d}}=\frac{\mathrm{2}\:\mathrm{sinh}\:\frac{{d}}{{x}}}{\frac{{d}}{{x}}} \\ $$$$\frac{{f}}{{d}}=\frac{\mathrm{cosh}\:\frac{{d}}{{x}}−\mathrm{1}}{\frac{{d}}{{x}}} \\ $$$${with}\:{t}=\frac{{d}}{{x}}\:{as}\:{parameter}: \\…

nice-calculus-prove-that-cos-pix-2-cosh-pix-dx-1-2-

Question Number 140831 by mnjuly1970 last updated on 13/May/21 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:……{nice}\:….\:{calculus}…… \\ $$$$\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\:\:\xi\::=\:\int_{−\infty} ^{\:\infty} \frac{{cos}\:\left(\pi{x}^{\mathrm{2}} \right)}{{cosh}\left(\pi{x}\right)}{dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:…. \\ $$$$\:\:\:\:……. \\ $$ Answered by…

Let-consider-A-lim-x-0-0-1-t-x-dt-1-x-Prove-that-A-0-1-ln-t-dt-Deduce-the-value-of-A-

Question Number 75228 by ~blr237~ last updated on 08/Dec/19 $$\:\mathrm{Let}\:\mathrm{consider}\: \\ $$$$\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} \left(\Gamma\left(\mathrm{t}\right)\right)^{\mathrm{x}} \mathrm{dt}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{A}=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\Gamma\left(\mathrm{t}\right)\right)\mathrm{dt}\:\: \\ $$$$\mathrm{Deduce}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{A} \\ $$ Commented…

Question-9686

Question Number 9686 by tawakalitu last updated on 24/Dec/16 Answered by mrW last updated on 24/Dec/16 $$\mathrm{u}=\mathrm{log}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \right) \\ $$$$\frac{\mathrm{du}}{\mathrm{dy}}=\frac{\mathrm{2y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} }×\mathrm{log}\:\mathrm{e}…