Evaluate using Maclaurin series expansion (only use the first 4 terms) So e axdx
7. (a) Use the well known Maclaurin series expansion for the cosine function: f (x ) = cos x = 1 x? 2! + 4! х 6! + (-1)" (2n)! . * 8! 0 and a substitution to obtain the Maclaurin series expansion for g(x) = cos (x²). Express your formula using sigma notation. (b) Use the Term-by-Term Integration Theorem to obtain an infinite series which converges to: cos(x) dx . y = cos(x²) (c) Use the remainder theorem associated...
10. (4 points) a. Use the Maclaurin series for function to find the first three nonzero terms of the Maclaurin series for the following function. b. Then use these terms (above) to approximate the integral 10.(4 points) a. Use the Maclaurin series for function f(x) = tan-?x to find the first three nonzero terms of the Maclaurin series for the following function g(x) = x tan-1x3. b. Then use these terms (above) to approximate the integral $0.5 x tan-1 x...
13 t5 + x7 12. The first 4 non-zero terms of the Maclaurin series for sin(x)= x - 3! 5! 7! Use those first 4 terms to evaluate sin( i ) (note: i= v=1, i? =-1, ...) Simplify as much as possible. sin( i ) (5)
a. Find the first four nonzero terms of the Maclaurin series for the given function. b. Write the power series using summation notation. c. Determine the interval of convergence of the series. f(x)=92 -2x a. The first nonzero term of the Maclaurin series is The second nonzero term of the Maclaurin series is The third nonzero term of the Maclaurin series is The fourth nonzero term of the Maclaurin series is b. Write the power series using summation notation. 00...
12. Use the Maclaurin expansion for e-t to express the function F(2) = dt as an alternating power series in 2. How many terms of the Maclaurin series are needed to approximate the integral for x=1 to within an crror of at most 0.001? Let
(1 point) Use a Maclaurin series derived in the text to derive the Maclaurin series for the function f(x) = 0. Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms. 1+x/18+X^2/600+x^3/35280
(4) Use MacLaurin series to evaluate the following limits. Do not use L'Hospital's rule. (a) lim-0 21+ucos g -3 sin e 136.23-1 (b) lim 0 sin(6x)(e-1-1)
Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 7x cos(2x2) (c) Use part (b) to find a power series for AUX) - 1621) 1x) - -1) ( 2.6 +1 +3 What is the radius of convergence, R? R-6 Find the Maclourin series for FUX) using the definition of a Maclaurin series. Assume that f has a power series expansion. Do not show that Ra(x) +0.1 Rox) = sin( Find the...
Write the first 4 non-zero terms of the Maclaurin series for: sin(- 2 x)/x