Question: Question 4. Using sin x=(1-cos(2x)), (a) Differentiate this series to obtain the Taylor series for sin(2x) about x = = 0. obtain the Taylor

Question 4. Using sin x=(1-cos(2x)), (a) Differentiate this series to obtain the

Question 4. Using sin x=(1-cos(2x)), (a) Differentiate this series to obtain the Taylor series for sin(2x) about x = = 0. obtain the Taylor series for sin x about x = 0. (b) Check your answer from (a) by finding the Taylor series for sin(2x) about x = way. (You may use any of the standard Taylor series derived in lectures). Question 5. Find the Taylor series of [(1-cos(2x)), *#0 x=0 f(x)= {(1 1 32 about = 0. Hence find f(7)(0) and f(8) (0). Question 6. Show that the Taylor series expansion for In(4+x2) about z = 0 is given by In(4+x) = 2 In 2+ + 1 192 x 0 in a different 2n n(22) 26 + = 2 In 2 + (-1)-1,

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