Combining power series Use the power series representation
to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.
35. f(3x) = ln (1 − 3x)
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Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Q// Consider the two series such that: f(x) = 1 + 2x + 3x2 +4x3 + ... and g(x) = 1 + 2x + 3x2 +4x3 + a. Find the sum of the two generating functions. Then find the generating function for the result. b. Find the product of the two generating functions. Attach File Browse My Computerarrow_forwardx²- Q6/ Find five terms of Maclaurin series for f(x) = (1 +x)K where (k) is any Real number, then find exact and approximate value of function if x = 1, k= 2 Ans./ f(x) = 1+ kx + k(k-1) k(k-1)(k-2) „3 1 k(k-1)(k-2)(k-3) ,4 2! 3! 4! @ x = 1 & k = 2 - Exact = 4 Аpproximate 3 4 Q7/ a) Find the first four nonzero terms of Maclaurin series for f (x) = e-x² b) Find the approximate value of the function in part (a) at x = and compare it with exact value? 2x2 12x 120x6 Ans./ a) f(x) =1- 2! +... 4! 6! 2 - Exact = 0. 64118 3 b) @ x == Approximate = 0. 6396 Q8) Considered that the function f(x) = x.e* i. Find the first three nonzero terms in Maclaurin series Compute the approximate value of function (Maclaurin series) at x = 1 and compare it with the exact value? Compute the approximate integral value of the function (Maclaurin series), ii. iii. Ans./ i)f(x) = x + x² +;x³ + ... ii) @ x = 1 - Approximate = 1+ 12 +1³ = 2.5 Exact = 1* e' = 2.7 iii) Integral = 0.958 Q9/ Answer the following points i.…arrow_forwardIn the image below.arrow_forward
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- 2+1 Recall that sin(x) = Σ(-1)" (2n+1)! Obtain the term of the power series of sin(x + 1) where n = 3 for a value of x = 3.20.arrow_forwardCalculus IIarrow_forwardUse the power series 1 1 + x f(x) = n = 0 to find a power series for the function, centered at 0. f(x) = In(x + 1) 80 ∞ n = 0 (−1)"x", |x| < 1 Determine the interval of convergence. (Enter your answer using interval notation.) (-1,1)arrow_forward
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