The taylor polynomial with 4 nonzero terms of The function f(x)=sin(4x)f(x)=sin(4x) has a maclaurin series. find the first 4 nonzero terms in the series is f(x) = 4x - (4x)³ + (4x)⁵ - (4x)⁷ + ...
3! 5! 7!
The taylor polynomial can be calculate as follows:
f(x) = sin(4x)
f' = 4cos(4x)
f'' = -16 sin(4x)
f''' = -64 cos(4x)
f⁽⁴⁾ = 256 sin(4x)
f⁽⁵⁾ = 1024 cos(4x)
The fourth-order Taylor series expansion is
f(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4! ) )f⁽⁴⁾(x) + ...
The Maclaurin series is obtained by setting x = 0.
Note that sin(0) = 0 and cos(0) = 1.
So the, The non-zero terms are:
f(h) = 4x - (4x)³ + (4x)⁵ - (4x)⁷ + ...
3! 5! 7!
your question is incomplete but most probably your full question was
The function f(x)=sin(4x)f(x)=sin(4x) has a maclaurin series. find the first 4 nonzero terms in the series, that is write down the taylor polynomial with 4 nonzero terms.
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In the development section of the sonata form, the tonal center changes frequently. What is this process called?.
The term when the tonal changes frequently in the development section of the sonata form is modulation.
What is Modulation in Sonata?Sonata is a type of musical composition that is played with only one instrument. In one sonata, there are usually 2 to 4 movements, each movement also has its own style of emotion. One of the most famous sonatas is Piano Sonata No. 14 by Ludwig van Beethoven which contains Moonlight Sonata. In sonatas, there is what is known as modulation. Modulation is basically the change from one tonality to another. Usually, modulation is also followed by changing the key signature.
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Which statement describes Plains hide artworks? A.
They have symmetry created from geometric shapes and patterns. B. They tell visual stories of trading with European explorers C.
They have decorations made of metal and clay beads. or D.
They show realistic animals of the Great Plains.
Plains hide artworks-They show realistic animals of the Great Plains.
What are Plains hide artworks?Plains hide painting is an artistic practice of the Plains Indians that involves painting on either tanned or raw animal hides. It was possible to paint tipis, tipi liners, shields, parfleches, robes, clothing, drums, and winter counts.
What is Geometric painting?Plains Traditionally, women create abstract, geometric motifs. Colors that were bright were desired, and spaces were filled with solid fields of color. Cross-hatching was only employed as a last option when the paint was short. Women discussed their designs in terms of their negative space, which was important. To break up large areas, dots are used.
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Neoclassical composers favored what musical quality? Multiple Choice Unusual and exotic scales Programmatic music Homophonic textures Clear polyphonic textures
The musical quality that neo-classical composers favor is clear polyphonic textures. Hence, the correct option is (D).
What are the Characteristics of Neo-Classical Music?Neo-classical music is a type of musical composition that emerged in the 1920s. This music also has some similarities with anti-romanticism. In simple terms, neoclassicism music uses references in the form of songs from the classical and baroque eras and rearranges these songs by changing the harmony, rhythm, and rhythm of these songs. In neoclassical songs, the composers also use a very clear polyphonic texture that allows us to hear several instruments simultaneously playing a note. One of the most influential neoclassical composers is Igor Stravinsky.
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