00 Use the power series representation f(x) = arctan(x) = Σ n=0 representation for g(x) = on the interval (-1, 1). (Hint: arctan(x) = x²) - 1+x² dx Select the correct answer below: 00 O 8(x) = (-1)"+¹2n O g(x) = n=0 00 Og(x) = (-1)"x²n-1 n=0 00 (-1)"x²n ○ 8(x) = (-1)"x²+1 n=0 00 (-1)" 2n+1-1

Q: Can the iteration xn+1 = cos (xn) be used to find the solu- tion of the equation cos (x) – x = 0 in…

A: Solution is given below

Q: find a power series representation for f(x) ln(14 -x)

A:

Q: Evaluate cos(x) – 1 + lim 2 12a4 Hint: Using power series.

A:

Q: O Let f (x) be a function which is represented by the power series f(x) =E(-1)"-1)". n3 What is the…

A: Power series of fx about x = a isfx = ∑n=0∞fnan!x-an              —⊛

Q: How to write sin(x)cos(3x) in power series

A: We need to write sin(x)cos(3x) in the power series. Taylor series of function fx at a is defined as:…

Q: help me with part e and f please

A:

Q: 18 Given the power series F(x)= 2 (-1)" (x-3)" n= 0 2" Find the derivative for the power series…

A: Answer to the question as follows:

Q: sinx x0 e²x-1 5. Use power series to evaluate lim

A: Power series expansion

Q: 1/16 Perform a test to determine if tan (80)d0 converges. b lim tan(80)d0 b-x/ 16" 0 (Simplify your…

A:

Q: x-14 Find the exact value of * dx. (x+4)(x-2) Select the correct answer below: 3 In(8/7) In(4) + 7…

A: we have to find the value of  ∫34 x-14x+4x-2dx

Q: Determine a power series representation for g(x)=x° cos(x). CoS

A: Solve the following