Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It...
6. For each given series, complete the following tasks: (i) Prove that the series converges ab- solutely; (i) Show that the series satisfies all conditions of the Alternating Series Test; (ii) Find the partial sum sy of the series, and then estimate its remainder Ra: (iv) Determine how many terms are needed to approximate the sum of the series accurate to within 0.001, and then find this approximation. (a) L (b) Σ 27! 6. For each given series, complete the...
Consider the following alternating series. (-1)*+ 1 3k k=1 (a) Show that the series satisfies the conditions of the Alternating Series Test. 1 3" Since lim o and an + 1 for all n, the series is convergent (b) How many terms must be added so the error in using the sum S, of the first n terms as an approximation to the sum n=10 X (c) Approximate the sum of the series so that the error is less than...
The Alternating Series Test and convergence. 8 = angle Pod sino g 3! as 3! a 7 " Functions can often be represented by an infinite series. A series reprezentation can help to solve differential equations, to fin derivatives, or to compute integrals involving the function. Computers also use these series representations to perform calculations. For example sin (0) 0 +... allows a calculator to give a decimal approximation of values of sine. Click here to access the Exo ore...
The Integral Test enables us to bound the error approximation of the series 1 (Inn)4 n=3 n by the partial sum 30 830 (In n)4 n=3_n What upper bound does it yield for the error s s3o ? Give your answer accurate to 3 significant digits. Number MIM8 The Integral Test enables us to bound the error approximation of the series 1 (Inn)4 n=3 n by the partial sum 30 830 (In n)4 n=3_n What upper bound does it yield...
Let Pbé à pósitive, continuous, and decreasing function for x 2 1, such that an-n). If the series an n 1 converges to S, then the remainder RN -S-Sw is bounded by Use the result above to approximate the sum of the convergent series using the indicated number of terms. (Round your answers to four decimal place Σ ,T, ten terms n2 +1' Include an estimate of the maximum error for your approximation. (Give your answer to four decimal places.)...
all but dont work on the julia box one which is 2 i think so 1-3-4 Fitchburg State University Department of Mathematics Project #3 Math 2400: Calculus II April 11, 2019 project for Calculus II. You may work on this with up to one other fellow student. Answer all questions completely and type or neatly write out. The final project should be turned in by Tueeday, April 23. How is it that we generate For this project it helps to...
13. 0/1.78 points | Previous Answers RogaCalcET3 10.6.052. My Note Use the power series for (1+x3)-1 and differentiation to find the power expansion for fx)-3X- 3x2 (x3 + 1)2 1 14. 0.46/1.86 points| Previous Answers RogaCalcET3 10.6.046. My Notes Ask Your Teacher Use the formula In(1 + x)- x- X23-*+.. for |x| <1 2 3 4 n-1 and your knowledge of alternating series to find the smallest N such that the partial sum Sy approximates In Confirm this using a...
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 answer all questions, I will rate you well. Thanks :) 14. 514 points | Previous Answers SCal:ET 11.11.021. Consider the following function. /(x) = x sin(x), a = 0, n = 4, -0.9 x 0.9 (a) Approximate fby a Taylor polynomial with degree n at the number a (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) * Tp(x) when x lies in the given interval. (Round M up to the nearest integer. Round your answer...
please help with all you can. answer 10 ill give a thumbs up! Question 1 A particular fruit's weights are normally distributed, with a mean of 263 grams and a standard deviation of 23 grams. The heaviest 4% of fruits weigh more than how many grams? Give your answer to the nearest gram. Submit Question Question 2 A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.9 years, and standard deviation of 1.1 years....