Mece 317 NuMod (Quiz 17-22) with Correct Answers

Mece 317 NuMod (Quiz 17-22) with Correct Answers The value of integral ∫(1 to 2)x*exp(1/x)dx using two-strips Trapezoidal Rule is - Ans:-2.9647 The error bound in estimating the value of integral ∫(1 to 2)x*exp(1/x)dx using one-strip Trapezoidal Rule is {assume that f"(x) is largest in magnitude at x =1 in the range} - Ans:-0.3 The two-strips Trapezoidal Rule of integration is exact for the following order polynomial - Ans:-first Using Trapezoidal Rule to estimate the integral ∫(0.2 to 2.2)x * exp(x) dx it was found that for h = 2, Area = 20.099; and for h = 1, Area = 14.034. Using Richardson Extrapolation, a better estimate is - Ans:-12.012 Using Trapezoidal Rule to estimate the integral ©GRACEAMELIA 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH OCTOBER 2024 Page 2/17 ∫(0.2 to 2.2)x * exp(x) dx it was found that for h = 1, Area = 14.034; and for h = 0.5, Area = 12.375. Using Richardson Extrapolation, a better estimate is - Ans:-11.822 Richardson Extrapolation provides two estimates that have truncation error proportional to h^4: for h = 2, Area = 19; and for h = 1, Area = 13. A better estimate will be - Ans:-12.6 Richardson Extrapolation provides two estimates that have truncation error proportional to h^6: for h = 2, Area = 19; and for h = 1, Area = 13. A better estimate will be - Ans:-12.9 Using the Trapezoidal Rule, we have three sets of estimates: h = 4, A = 18; h = 2, A = 16; and h = 1, A = 13. The best approximation using Romberg Integration is - Ans:-11.78 Using h = 1 and Simpson's One-Third Rule, the approximate value of the following integral is ∫(0.2 to 2.2)x * exp(x) dx - Ans:-12.012 Using h = 1 and Simpson's One-Third Rule, the truncation error bound in the approximating of the following integral is ∫(0.2 to 2.2)x * exp(x) dx - Ans:-0.7 Using the O(h) Forward Difference formula with a step size h = 0.2, the first derivative of the function f(x) = 5e^2.3x at x = 1.25 is - Ans:-258.8 ©GRACEAMELIA 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH OCTOBER 2024 Page 3/17 We are using the O(h) Backward Difference formula to estimate the first derivative f'(x) at x = 1.75 where f(x) = e^x using a step size h = 0.05. If we keep halving the step size h to obtain 2 significant digits in f'(x), without any extrapolations, the final step size h will be - Ans:-0.05/8 Given the following table of values, the first derivative f'(x) at x = 0.7 using Central-Difference O(h^2) formula is x 0.6 0.7 0.8 0.9 1.0 f(x) 3.1767, 2.9209, 2.7923, 2.7340, 2.7183 - Ans:--1.9920 Given the following table of values, the first derivative f'(x) at x = 0.7 using Forward-Difference O(h^2) formula is x 0.6 0.7 0.8 0.9 1.0 f(x) 3.1767, 2.9209, 2.7923, 2.7340, 2.7183 - Ans:--1.6375 ©GRACEAMELIA 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH OCTOBER 2024 Page 4/17 Given the following table of values, the second derivative f''(x) at x = 0.7 using Central-Difference O(h^2) formula is x 0.6 0.7 0.8 0.9 1.0 f(x) 3.1767, 2.9209, 2.7923, 2.7340, 2.7183 - Ans:-12.7200 Given the following table of values, the second derivative f''(x) at x = 0.7 using Forward-Difference O(h^2) formula is x 0.6 0.7 0.8 0.9 1.0 f(x) 3.1767, 2.9209, 2.7923, 2.7340, 2.7183 - Ans:-9.8000 Given the following table of values, the first derivative f'(x) at x = 0.9 using Central-Difference O(h^2) formula is ©GRACEAMELIA 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH OCTOBER 2024 Page 5/17 x 0.6 0.7 0.8 0.9 1.0 f(x) 3.1767, 2.9209, 2.7923, 2.7340, 2.7183 - Ans:--0.3700 Given the following table of values, the first derivative f'(x) at x = 0.9 using Backward-Difference O(h^2) formula is x 0.6 0.7 0.8 0.9 1.0 f(x) 3.1767, 2.9209, 2.7923, 2.7340, 2.7183 - Ans:--0.2315 Given the following table of values, the second derivative f''(x) at x = 0.9 using Centra