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Category: Differentiation

Nice-Calculus-prove-that-x-n-1-a-n-sin-nx-n-e-acos-x-sin-asin-x-m-n-

Question Number 141057 by mnjuly1970 last updated on 15/May/21 $$ \\ $$$$\:\:\:\:\:\:\:…..\mathscr{N}{ice}\:……\:\:……\mathscr{C}{alculus}….. \\ $$$$\:\:\:{prove}\:{that}: \\ $$$$\:\Omega\left({x}\right):=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}^{{n}} .\frac{{sin}\left({nx}\right)}{{n}!}={e}^{{acos}\left({x}\right)} {sin}\left({asin}\left({x}\right)\right) \\ $$$$\:\:\:….{m}.{n} \\ $$ Answered…

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…