A graphing calculator is recommended. Find the Maclaurin series of f (by any method). Rx) = costx?) Find the radius of convergence, R. R 00 Graph fand its first few Taylor polynomials on the same screen. 1.5
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- 8x3 Find the power series for f(x) = in the form an. (1 - x*) n=1 Hint: First, find the power series for g(x) = 2 Then differentiate. 1 – x4 (Express numbers in exact form. Use symbolic notation and fractions where needed.) an =00 12x Find a power series for f(x) = |x| an. (x2 + 1)" n=1 -1 Hint: First, find the power series for g(x) (1 + x2) and then differentiate. (Express numbers in exact form. Use symbolic notation and fractions where needed.) an =Find the first four nonzero terms of the Maclaurin series for the function by multiplying or dividing the appropriate power series. Use the table of power series for elementary functions. sin(x) g(x) 1 + x P4(x) = Use a graphing utility to graph the function and its corresponding polynomial approximation. O = -6 -4 4 4 6 6 6- 4- 2-
- Find the first four nonzero terms of the Maclaurin series for the function by multiplying or dividing the appropriate power series. Use the table of power series for elementary functions on . Use a graphing utility to graph the function and its corresponding polynomial approximation. f(x) = ex /(1 + x)15x2 Differentiate the power series for g(x) = 5 to obtain a power series for f(x) = 1- x3 (1 – x³)* Write the general term a, in the form E an. (Express numbers in exact form. Use symbolic notation and fractions where needed.) an =20x3 Find the power series for f(x) in the form An. (1 – x4)* n=1 5 Hint: First, find the power series for g(x) Then differentiate. x4 (Express numbers in exact form. Use symbolic notation and fractions where needed.) An =
- Find the power series for the function using the suggested method. Use the basic list of power series for common functions. Use the power series for x + 1 3x f(x): x + 18x Find a power series for f(x) |x| an. (x2 + 1) n=1 -1 Hint: First, find the power series for g(x) = (1+ x²)¯' and then differentiate. (Express numbers in exact form. Use symbolic notation and fractions where needed.) An =Find the power series for f(x) = ∞ 24x3 in the form Σ (1-x4)² Σα n=1 Hint: First, find the power series for g(x) an = = 6 an. Then differentiate. x4 (Express numbers in exact form. Use symbolic notation and fractions where needed.)
- 1/2 Find the first four terms of the binomial series for the function (1+ 9x) The first four terms areFind the first four nonzero terms of the Maclaurin series for the function by multiplying or dividing the appropriate power series. Use the table of power series for elementary functions on . Use a graphing utility to graph the function and its corresponding polynomial approximation. h(x) = (cos x) ln(1 + x)Find the Maclaurin series for f(x) = cos (x'). %3D (Use symbolic notation and fractions where needed.) cos (x³) = > -1)" (x*) (-1)" „ón 2n! Incorrect Use the found series to determine f((0). (Use decimal notation. Give your answer as a whole or exact number.) 6(0)%3D -360