Approximate In(1.05) with an accuracy of 0.0000000001. Show (1) the derivation of the Taylor series about a=1, (2) the computation for determining the number of terms needed to achieve the desired accuracy and (3) the value of the approximation.

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A: Taylor series for f(x) at a  is given by…

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A: Here, use the power series expansion of the function 11-x is: 11-x=∑n=0∞xn...(1)

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Q: Approximate ln 0.5 using three terms of the Taylor series expansion of ln(1−x) about 0.

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Q: Given f(x) = e® (a) Find its Taylor series for à = 2. (b) Find the interval and radius of…

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Q: The Taylor series for f(x) = e" at a = -4 is > Cn (x + 4)". %3D n=0 Find the first few coefficients.…

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Q: The Taylor series for f(x) = In(sec(2) at a = 0 is Σ (2)". n=0 Find the first few coefficients. co=…

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