Формула Тейлора (примеры)

Пример 6

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y = sin(sin x)

y′ = cos(sin x)cos x

y″ = −sin(sin x)cos² x − cos(sin x)sin x

y′′′ = −cos(sin x)cos³ x + 3sin(sin x)cos x sin x − cos(sin x)cos x

y^(IV) = sin(sin x)cos⁴ x + 6cos(sin x)cos² x sin x −

−3sin(sin x)sin² x + 4sin(sin x)cos² x + cos(sin x)sin x

y^(V) = cos(sin x)cos⁵ x − 10sin(sin x)cos³ x sin x −

−15cos(sin x)cos x sin² x + 10cos(sin x)cos³ x −

−15sin(sin x)sin x cos x + cos(sin x)cos x

y(0) = 0, y′(0) = 1, y″(0) = 0, y′′′(0) = −2, y^(IV)(0) = 0, y^(V)(0) = 12