Найти [tex]\frac{d^2y}{dx^2}[/tex] функции [tex]\left \{ {{x=3(t-sint)} \atop {y=4(1-cost})} \right.[/tex]. Created by Nik133. algebra-ru

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Nik133 @Nik133

August 2022 1 50 Report

Найти [tex]\frac{d^2y}{dx^2}[/tex] функции

[tex]\left \{ {{x=3(t-sint)} \atop {y=4(1-cost})} \right.[/tex]

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dtnth

Verified answer

$x=\phi (t);\\ y=\psi (t);\\ y'_x=\frac{\psi'(t)}{\phi'(t)};\\ y''_{x^2}=\frac{\psi''(t)\phi '(t)-\psi'(t)\phi''(t)}{(\phi'(t))^3}$

$x'_t=3-3cost;\\ x''_{t^2}=3sint;\\ y'_t=4sint;\\ y''_{t^2}=4cost;$

$y''_{x^2}=\frac{4cost(3-3cost)-4sint *3sint}{(3-3cost)^3}=\\ \frac{12cost-12(cos^2 t+sin^2 t)}{27(1-cost)^3}=\\ \frac{12cost-12*1}{27(1-cost)^3}=\\ \frac{-12(1-cost)}{27(1-cost)^3}=\\ \frac{-4}{9(1-cost)^2}$

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Answers & Comments

Verified answer

reshit zadachu na ekstremum chislo a rozlozhit na dva mnozhitelya tak chtoby ih sum

tex i obyasnite pozhalujsta kak reshat podobnogo roda zadaniya

v yashike est detali sdelannye na tryoh stankah veroyatnost togo chto detal sde

m na prodolzhenii osi sterzhnya na rasstoyanii 20 sm ot blizhnego konca sterzhnya razm

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tex tolko pozhalujsta ochen podrobno

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