Taylor's Theorem to Find the First Four Terms of the Series

question 41

Multiple Choice

Taylor's Theorem to find the first four terms of the series solution of $y ^ {t } - 2 x y = 0$ given the initial condition $y ( 0 ) = 1$ and use it to calculate $y ( 3 )$ . Round your answer to three decimal places wherever applicable.

• A) \(y = 1 + \frac { 2 } { 2 ! } x + \frac { 12 } { 4 ! } x ^ { 2 } + \frac { 120 } { 6 ! } x ^ { 3 } + \cdots ; y ( 3 ) \approx 13.000\)
• B)\(y = 1 + \frac { 1 } { 2 ! } x ^ { 2 } + \frac { 6 } { 4 ! } x ^ { 4 } + \frac { 60 } { 6 ! } x ^ { 6 } + \cdots , y ( 3 ) \approx 86.500\)
• C)\(y = 1 + \frac { 2 } { 1 ! } x ^ { 2 } + \frac { 12 } { 2 ! } x ^ { 4 } + \frac { 120 } { 3 ! } x ^ { 6 } + \cdots , y ( 3 ) \approx 15,085.000\)
• D) \(y = 1 + \frac { 2 } { 2 ! } x ^ { 2 } + \frac { 12 } { 4 ! } x ^ { 4 } + \frac { 120 } { 6 ! } x ^ { 6 } + \cdots ; y ( 3 ) \approx 172.000\)
• E) \(y = 1 + \frac { 2 } { 1 ! } x + \frac { 12 } { 2 ! } x ^ { 2 } + \frac { 120 } { 3 ! } x ^ { 3 } + \cdots , y ( 3 ) \approx 601.000\)

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