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without approximating and calculator A B e34 1 Write : dx as a series. 2 2...
without approximating answers and without using calculator solve following: A B C Find the area between y = x and y = x2 with 0 < x <4 . Find the volume of the surface of revolution created by revolving the region bounded by y = x2 +1, y = 9 - 22, around the line y = -1. . A 1600 pound elevator is suspended by a 200 foot cable with a weight of 10 pounds per foot. Find...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is given by r" for 1 sts 6 a) Use the ratio test to find the interval of convergence of the Maclaurin series for f a) Find the slope of the line tangent to the curve C at the point where t 3. b) Let...
If f has a continuous second derivative on [a, b], then the error E in approximating by the Trapezoidal Rule is (b- a 12n rmax x)1. asxsb. JE s Moreover, if f has a continuous fourth derivative on [a, bl, then the error E in approximating by fix) dx Simpson's Rule is b-a)s 180a lrmax (x. asxsb. Use these to find the minimum integer n such that the error in the approximation of the definite integral is less than or...
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...
Write the Maclaurin series for f(x)=8cos4x2 as n=0cnxn Find the following coefficients. Write the Maclaurin series for f(x) = 8 cos(4x) as Conten. n=0 Find the following coefficients. II Co C2 = C4 C6 = Cg =
(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
Consider the integral 1 To vita dx V1 + x3 (a) Write out the first four non-zero terms of the MacLaurin series for the above integral. (b) Write out the first four non-zero terms of the series for 1 so dx V1 + x3 (c) How many terms of the above series should we add together to estimate p1/2 dc V1 + x3 within 0.001? 1
If f has a continuous second derivative on tə, b), then the error E in approximating f(x) dx by the Trapezoidal Rule is IELS (-a) [max 1f"(x)), a sxs b. 12n2 Moreover, if f has a continuous fourth derivative on (a, b), then the error E in approximating Rx) dx by Simpson's Rule is IES (6-a) [max 1(1)(x)), a sxs b. 1804 Use these to find the minimum Integer n such that the error in the approximation of the definite...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered at T. 15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered...
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...