Approximating definite
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- slovearrow_forwardS1 please help me with the brief solution and answer, thank youarrow_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
- Please solution speedarrow_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_forwardI send the question several times and pay, but it seems that you do not deserve respect. I said several times, please circle the answer and write it correctly if you write by hand.arrow_forward
- ex -1arrow_forwardQ3. Define Fourier Series. Find the Fourier sine series of the function f(x) = kx2, 0 < x < k. Sketch f(x) and its periodic extensions. Show the answer in details.arrow_forward16 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_forwarda=0arrow_forwardUse Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the value of the error. (Round your answers to three significant figures.) sinh(0.6) ≈ 0.6 + ((0.6)3 /3!)arrow_forward(a) Find a power series for the function f : (0, 0) → R given by f(x) = $in² about the point x = A. Hint: The Taylor series for xH sin x may be helpful. 2. = B. (b) Find the Taylor series for the function f : (0, 00) → R given by f(x) = log x about the point x =arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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