Approximating definite
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- HELP ME PLSarrow_forwardslovearrow_forwardI send the question a second time and pay for each question. Can I explain to you how to write the answer correctly? How can I explain that you write by hand, it is very bad and unreadable? Please give the final answer and you already answered it wrong.arrow_forward
- Evaluate the indefinite integral as an infinite series. cos(x) – 1 dx х n = 1 Need Help? Talk to a Tutor Watch Itarrow_forwardI need the answer as soon as possiblearrow_forwardUse series to approximate the definite integral to within the indicated accuracy: sin(x) dx, with an error < 10 4 Note: The answer you derive here should be the partial sum of an appropriate series (the number of terms determined by an error estimate). This number is not necessarily the correct value of the integral truncated to the correct number of decimal places. 0.234arrow_forward
- 16 dz 2 + 4 (a) Evaluate the integral: Your answer should be in the form kr, where k is an integer. What is the value of k? Hint: arctan(z) | r2 +1 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 16 f(=) Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. r2 + 4 What are the first few terms of S? a, = 32 a2 = 20 128 az = 112 512 a4 = 576 of of ofarrow_forward(a) Evaluate the integral: Hint: = Your answer should be in the form kn, where k is an integer. What is the value of k? d dx —arctan(r) a₁ = a2 = 2 16 x² + 4 · 6²³ a3 = (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 16 f(x) = x² + 4 What are the first few terms of S? ao= a4 = dr 1 I²+1 (c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of in terms of an infinite series. Approximate the value of by the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 12 terms? (Use the alternating series estimation.)arrow_forward1/10 11. Approximate the definite integral dz to within an error of at most 10- Hint: Use the Maclaurin series of e- to write the integral as an alternating series. write cach of the following complex pumbers in the form a+barrow_forward
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