For problems 1 & 2 use one of the Taylor Series derived in the notes to determine the Taylor Series for the given function. 1. f(x) = cos(4x) about x = 0 2. f(x) = x^6e^{2x^3} about x = 0 For problem 3 – 6 find the Taylor Series for each of the following functions. 3. f(x) = e^{-6x} about x = -4 4. f(x) = ln(3 + 4x) about x = 0 5. f(x) = 7/x^4 about x = -3 6. f(x) = 7x^2 - 6x + 1 about x = 2
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f(x) = cos(4x) about x = 0 We know the Taylor series for cos(x) is given by: cos(x) = Σ (-1)^n * (x^(2n)) / (2n)! for n = 0 to infinity To find the Taylor series for cos(4x), we can substitute 4x in place of x in the above series: cos(4x) = Σ (-1)^n * (4x)^(2n) / Show more…
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