Taylor series. Please show all work neatly. Thanks! 2. In the course of some physics problem...
please show all work and dont forget to evaluate the intefral Use a Taylor series to approximate the following definite integral. Retain as many terms as needed to ensure the error is less than 10-4. 0.33 S s in (1+x2) dx 0 Rewrite the given integral using a Taylor series and simplify the result. Choose the correct answer below. 0.33 0.33 x4 x4 OA X- x² ² 2! 3! + dx B. X- x² x² 2 3 + +.. dx...
Please help with 1-10 and please show all work thanks. Show all of your work neatly, and express solutions as exact answers unless otherwise requested. No credit will be given to solutions that have no work shown! BOX or CIRCLE your final answer. 1. Sketch a graph and shade the area of the region bounded by the following equations. Set up an integral that would give this area. 2x + y2 = 6 and y=x+1 2. Sketch a graph and...
Please show the work for each practical parts. Thanks 8. a) Write at least the first 4 terms of a Taylor(Maclaurin) Series centered at O for f(x)=es (Recall that in the previous question, you developed a series for $(x)=e) (7 pts.) b) Evaluate * dx using the series you generated in part a) (use 4 terms) (10pts) (4 pts.) c) Determine the approximate error of your answer in part b)
Please answer all, be explanatory but concise. Thanks. Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
Please show work, thanks. (2) Express the solution of the given initial-value problem in terms of an integral-defined function. 3,94 + (6 cosa)y=f, y0)=1
Problem 4. Using the Taylor series representation of Logz from the last part of Problem 3, show that the function \수, zメ0,2メ1, and-r < Arg(z) < π is analytic in its domain Problem 5. Use multiplication of power series in order to find the Taylor series expansion up to 24 of the function e2 22+1 with center at the origin. On what disk is the Taylor series convergent? Problem 6. Use division of power series in order to find the...
Please solve all. Show all of your work! 1. Find a power series representation of the function f(0) = x arctan(2.c) and determine the raidus of convergence. 2. Let f(x) = 1 + r. (a) Find the Maclaurin series of radius of convergence? (ie the Taylor series centered at a = 0). What is the (b) Find the Taylor series of centered at a = 3. What is the radius of convergence?
Please show ALL work and steps and an explanation as to why the series is convergent or divergent Use the Integral Test to determine whether the series is convergent or divergent. oo -5n ne n = 1 Evaluate the following integral. -5x dx 59 xe Since the integral ---Select--- finite, the series is ---Select--- -
i need help for these 2 question, please show your work, thanks 7) Determine whether the integral is convergent or divergent. Evaluate the integral if it is convergent. J. Vīt 3 dx 9) Evaluate the integral below.
please show all work neatly! also this is a differential eqaution problem