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(Solved): The Taylor series expansion for tant is tant=t+3t3+152t5+31517t7+t<2 Use ...



The Taylor series expansion for \( \tan t \) is
\[
\tan t=t+\frac{t^{3}}{3}+\frac{2 t^{5}}{15}+\frac{17 t^{7}}{315}+\cdots \q

The Taylor series expansion for is Use the first three terms in the series to obtain an approximate closed-form solution of the following problem over the interval . Compare your answer at with that obtained in Example 2.7.6, which was obtained by using two terms in the series.


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To obtain an approximate closed-form solution of the problem using the first three terms of the Taylor series expansion for tangent, we can substitute
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