0.5 22. (a) Express. da as an infinite series. do not evaluate! 사9r6 r0.5 3 (b)...
How to do part (c) and part(d)? How to do part (c) and part(d)? (a) Evaluate the integral 2 48 dx Your answer should be in the form kr, where k is an integer. What is the value of k? darctan(x dx r2+1 (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x)-Then, integrate it from o to 2, and call it S. S should be an infinite series. What are...
4) Evaluate dx (4 – x²) 3/2 5) Evaluate the improper integral ſxe**dx 0 6) Express the repeating decimal 0.123 as a geometric series and then use the sum of that series to express the decimal as the ration of two integers.
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...
22 . . 23 . 24 Use the binomial series to expand the function as a power series. 7 (4 + x) 3 Σ Your answer cannot be understood or graded. More Information n = 0 X State the radius of convergence, R. R = 4 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(4x) D) n = 0 Evaluate the indefinite integral as an infinite series. I conte...
Programming Assignment 3 CSCI 251, Fall 2015 Infinite Series Trigonometric and math functions are usually calculated on computers using truncated Taylor series (an infinite series). An infinite series is an infinite set of terms whose sum is a particular function or expression. For example, the infinite series used to evaluate the natural log of a number is (x - 1)2 (x-1)3 (x-1)* (x-1)5 2 4 where x E (0, 2], or 0
help me with this. (1 point) (a) Evaluate the integral Your answer should be in the form kT, where k is an integer. What is the value of k? (Hint: darctan(z)- dr 2+1 tb) Now, lets evaluate the same integral using power series. First, find the power series for the function f(). Then, integrate it from 0 to 2, and call it S. S should be an infinite series an What are the first few terms of S 16 2+4...
6) Use a Taylor series to estimate the integral's value to within an error of magnitude less than 10-3 0.7 In(x2 + 1)dx 6) Use a Taylor series to estimate the integral's value to within an error of magnitude less than 10-3 0.7 In(x2 + 1)dx
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...
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...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...