(1 point) Let F(z) = [" sin(4t) dt. Find the MacLaurin polynomial of degree 7 for...
t F(x)=∫x0sin(7t2) dt. Find the MacLaurin polynomial of degree 7 for F(x). 7/3x^3-49/6x^7 Use this polynomial to estimate the value of ∫0.750sin(7x2) dx. -0.105743 (1 point) Let F(x)sin(7t2) dt. Find the MacLaurin polynomial of degree 7 for F(x) 713xA3-49/6x7 0.75 Use this polynomial to estimate the value of sin(7x2) dx 0.105743 Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 50%. (1 point)...
-1/3 (i) Find the third-degree Maclaurin polynomial Tz(x) for f(x)= (1+4x). You can use differentiation or derive the polynomial using binomial series. (ii) Find approximation errors|f(x)– Tz(x) at x =0.1 and x=1.
Let f(z-y2 sin(x+-) Answer the following. Show and explain your work. (a) Find the Taylor polynomial of order 4. generated by f(x) at zo (b) Describe the MacLaurin series of f (with or without the sigma notation). (Hint: What pattern do the derivatives of f at z-0 follow?) (c) Does the MacLaurin series of f converges absolutely, converges conditionally or diverges at -1? Let f(z-y2 sin(x+-) Answer the following. Show and explain your work. (a) Find the Taylor polynomial of...
1,2,3, and 4 Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Problem 2 Let f(x) = sin 2x and P() be the interpolation polynomial off with degree n at 20,***, Im Show that \,f(z) – P() Sin+1 – 20) (1 - 11). (I – In).
n+ 1 1.8221 (0.6)" < 0.001 By trial and error, n 5. 39 (a) Compare the Maclaurin polynomials of degree 4 and degree 5, respectively, for the functions f(x)e and g(x)- e What is the relationship between them? (b) Use the result in part (a) and the Maclaurin polynomial of degree 5 for f(z) = sinz to find a Maclaurin polynomial of degree 6 for the function g(x)sin r (c) Use the result in part (a) and the 5 for...
3) Let F(x) = {* In In(1+t) dt. t (a) Find the Maclaurin series for F: (b) Use the series in part (a) to evaluate F(-1) exactly and use the result to state its interval of convergence. (c) Approximate F(1) to three decimals. (Hint: Look for an alternating series. )
(a) Find the third-degree Taylor polynomial for f() = x3 +7x2 - 5x + 1 about 0. What did you notice? (b) Use a calculator to calculate sin(0.1)cos(0.1). Now, using the second-order Taylor polynomial, give an estimate for sin(0.1) cos (0.1). Estimate the same expression using the third-order Taylor polynomial, and compare the two approximations. Note that your estimates should be rounded to seven digits after the decimal place. (a) Find the third-degree Taylor polynomial for f() = x3 +7x2...
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation: (I point) Let F=21+(z...
(1 point) Find the polynomial of degree 9 (centered at zero) that best approximates f(x) = ln(° +5). Hint: First find a Taylor polynomial for g(x) = ln(x + 5), then use this to find the Taylor polynomial you want 1/2 Now use this polynomial to approximate L'iniz? +5) da. -1/2 Lis(z) dx =