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

 

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Question 4. Using sin² x=(1-cos(2x)), (a) Differentiate this series to obtain the Taylor series for sin(2x) about x = = 0. obtain the Taylor series for sin² 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(2x²)), *#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+x²) = 2 In 2+² + 1 192 x 0 in a different 2n n(22) 26 ³+ = 2 In 2 + (-1)-1, Question 4. Using sin² x=(1-cos(2x)), (a) Differentiate this series to obtain the Taylor series for sin(2x) about x = = 0. obtain the Taylor series for sin² 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(2x²)), *#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+x²) = 2 In 2+² + 1 192 x 0 in a different 2n n(22) 26 ³+ = 2 In 2 + (-1)-1,

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ANSWER ATTACHED IMAGE 4 sin x 1 cos 2x 2 1082x the taylors series expansion of cos 2x about x 0 i... View the full answer