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

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©GRACEAMELIA 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED

FIRST PUBLISH OCTOBER 2024




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




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, ©GRACEAMELIA 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED

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∫(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



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, ©GRACEAMELIA 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED

FIRST PUBLISH OCTOBER 2024




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




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