Mece 317 NuMod Practice Questions
With Solution
The value of integral ∫(1 to 2)x*exp(1/x)dx using two-strips Trapezoidal Rule
is - ANSWER 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} - ANSWER 0.3
The two-strips Trapezoidal Rule of integration is exact for the following order
polynomial - ANSWER 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 - ANSWER 12.012
Using Trapezoidal Rule to estimate the integral
∫(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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 -
ANSWER 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 - ANSWER 258.8
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 - ANSWER 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 - ANSWER -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 - ANSWER -1.6375
Given the following table of values, the second derivative f''(x) at x = 0.7
using Central-Difference O(h^2) formula is
With Solution
The value of integral ∫(1 to 2)x*exp(1/x)dx using two-strips Trapezoidal Rule
is - ANSWER 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} - ANSWER 0.3
The two-strips Trapezoidal Rule of integration is exact for the following order
polynomial - ANSWER 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 - ANSWER 12.012
Using Trapezoidal Rule to estimate the integral
∫(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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 - ANSWER 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 -
ANSWER 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 - ANSWER 258.8
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 - ANSWER 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 - ANSWER -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 - ANSWER -1.6375
Given the following table of values, the second derivative f''(x) at x = 0.7
using Central-Difference O(h^2) formula is
