Note: Please show your intermediate steps; you cannot get full credits with only a final answer. 1. a. Round the following numbers to 4 digits, then find the absolute error and relative error: i) 4.86544 ii) 124.57016 iii) -12.39953 b. Suppose the numbers in part a are obtained by the k-digit rounding approach. Compute the absolute error bounds for each approximated number in part a. 2. a) Give the computational representations (in terms of decimal representations) of the following integer variables: i) 2024 ii) -730160 b) Give the floating-point representation of the following numbers: i) -54.6453873 ii) 0.0000635 iii) 1368.6217124 c) Find the absolute error and relative error for the floating point representation of the numbers in part b. d) Convert 132 to the binary number.
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86544 rounds to 4.8654 ii) 124.57016 rounds to 124.5702 iii) -12.39953 rounds to -12.3995 Show more…
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9.2 #7 . For Part C, PLEASE round to the nearest 4 decimal places!!
Oswaldo J.
Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places. Use the rounded values for subsequent calculations.) y' = y, y(0) = 1; y(1.0) y(x) = (explicit solution) h = 0.1 xn yn Actual Value Absolute Error % Rel. Error 0.00 1.0000 1.0000 0.0000 0.00 0.10 1.1052 0.20 1.2214 0.30 1.3499 0.40 1.4918 0.50 1.6487 0.60 1.8221 0.70 2.0138 0.80 2.2255 0.90 2.4596 1.00 2.7183
Adi S.
Note: for this problem, because later answers depend on earlier ones, you must enter answers for all answer blanks for the problem to be correctly graded. If you would like to get feedback before you completed all computations, enter a "1" for each answer you did not yet compute and then submit the problem. (But note that this will, obviously, result in a problem submission.) (a) What is the exact value of ∫₀⁴ eˣ dx? ∫₀⁴ eˣ dx = e^4-1 (b) Find LEFT(2), RIGHT(2), TRAP(2), MID(2), and SIMP(2); compute the error for each. LEFT(2) value 16.778, error [(e^(4))-(16.778)] RIGHT(2) value 123.974, error [(e^(4)-123.974)] TRAP(2) value 70.376, error -16.778 MID(2) value 45.607, error 7.99 SIMP(2) value 56.769, error -3.171 (c) Repeat part (b) with n = 4 (instead of n = 2). LEFT(4) value 31.193, error [e^(4)-31.193] RIGHT(4) value 84.791, error [e^(4)-84.791] TRAP(4) value 57.99, error -4.394 MID(4) value 51.428, error 2.17 SIMP(4) value 53.864, error -0.266 (d) For each rule in part (b), as n goes from n = 2 to n = 4, does the error go down approximately as you would expect? Explain by calculating the ratios of the errors: Error LEFT(2)/Error LEFT(4) = 1.643 Error RIGHT(2)/Error RIGHT(4) = 2.256 Error TRAP(2)/Error TRAP(4) = 3.818 Error MID(2)/Error MID(4) = 3.682 Error SIMP(2)/Error SIMP(4) = 11.921 (Be sure that you can explain in words why these do (or don't) make sense.)
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