Numerical Methods
Showing 226-256 of 256 answers
Using Secant method, what is the value of the next approximated root x2 if x0 = -3 and x1 = 1 for the function f(x) = x3+ 4x+8
- -07096
- -06736
- 02727 Correct
- -04961
Using the Maclaurin series expansion of cos(x) , when x = will give an approximate value of 0.6073 using the first two terms only.
- True Correct
- False
What is the effect of using multiple segment trapezoidal rules to an exponential function?
- an n increases, the error also increases
- as n decreases, the error decreases
- as n increases, the error decreases Correct
- using multiple n segment has no significant in Trapezoidal rule
What is the next approximated root for the function f(x) = ex + sin(x) when x0 = 0?
- Invalid initial value Correct
- 05
- -05
- 1
What is the next approximated root for the function f(x) = x + cos(x) when x0 = 0?
- 0 Correct
- -07391
- -1
- 1
What is the suppose the interval is from [05, 25] and n = 4?
- 0125
- 1
- 05 Correct
- 075
What is the value of the inverse of a matrix if the determinant of the main matrix is zero?
- no correct answer
- doesn't exist Correct
- zero
- infinite
When it comes to computer implementation, secant method may have an advantage over the Newton-Raphson since the latter only evaluates the function and not its derivative.
- True Correct
- False
When it comes to computer implementation, secant method may have disadvantage over the Newton-Raphson since Secant method depends on the previous approximation making it slower than the Newton Raphson
- True Correct
- False
When the exact value is π = 3.14159265359 and the relative error is given as 0.001, the approximate value is ____________.
- 3141606813
- 3141706813
- 3141890681
- 3141906813 Correct
Which among the following cases would give a different step size?
- a = 0; b = 1; n = 5
- a = 0; b = 2; n = 10
- a = 0; b = 6; n = 12 Correct
- a = 1; b = 5; n = 20
Which among the given set of values provides the least approximation error in employing trapezoidal rule?
- f(x) = 2 sin 21x; n = 5
- f(x) = sin 35x; n =20 Correct
- f(x) = 2cos 35x; n = 10
- f(x) = cos 21x; n = 15
Which among the given set of values will produce the closest value(for a = 0 and b = 4)?
- f(x) = cos 21x; h = 15
- f(x) = 2 sin 21x; h = 20
- f(x) = sin 35x; h =05 Correct
- f(x) = 2cos 35x; h = 10
Which initial value can get the next approximated value of the root equal to 1 if f(x) = ex
- no correct answer
- -1
- 1
- 0 Correct
Which is true about the error when approximating the integral of the linear function f(x) = 3x for an interval of [0,1]?
- The error in Trapezoidal rule is half of that in Simpson's rule
- The error is larger using Simpson's 1/3 rule compared to Trapezoidal rule
- The error is smaller using Simpson's 1/3 rule compared to Trapezoidal rule
- The error is equal to zero using Simpson's 1/3 rule compared to Trapezoidal rule Correct
Which of the following is the best initial guess for the function f(x) = e x – sin x
- Π
- 1 Correct
- 05
- 0
Which of the following correctly describes an algorithm?
- Algorithm is being used to determine the most practical kinds of solution to solve a problem
- All of these Correct
- It is an efficient method that can be expressed within finite amount of time and space
- An algorithm is a set of steps of operations to solve a problem performing calculation, data processing, and automated reasoning tasks
Which of the following is considered an open method?
- Gauss-Seidel
- Secant method Correct
- Cholesky's factorization
- No correct answer
Which of the following is not true in finding the determinant of a matrix?
- It doesn’t work with non-square matrix
- Coefficients from systems of linear equations may form a matrix and could be used for finding the determinant
- The operation between the matrices also takes an alternate sign of negative first then positive Correct
- No correct answer
Which of the following is the best application of approximating an integral of a function numerically?
- an elementary function
- a function whose anti derivative cannot be found Correct
- a polynomial function
- an exponential function
Which of the following is the first step in solving computational problems?
- Designing an Algorithm
- Development of a model
- Specification of an Algorithm
- Problem definition Correct
Which of the following is true about A - B?
- Subtraction of matrices is not possible Correct
- The resulting matrix A - B is a 3 x 2 matrix
- A - B is the same as B - A
- All of the answers correct
Which of the following is true about A x B?
- The resulting matrix, A x B is a 2 x 4 matrix
- All of the answers correct
- A x B is the same as B x A
- Matrix multiplication is not possible Correct
Which of the following is true about the determinant of A and B when
- The absolute value of the determinant is 1
- Neither "the determinant of A is the inverse sign of B" nor "the absolute value of the determinant is 1" is correct
- The determinant of A is the inverse sign of B
- Both "the determinant of A is the inverse sign of B" and "the absolute value of the determinant is 1" are correct Correct
Which of the following is true about the determinant of A when
- The absolute value of the determinant is 1
- Both "the determinant is negative" and "the absolute value of the determinant is 1" are correct Correct
- Neither"the determinant is negative" nor "the absolute value of the determinant is 1" is correct
- The determinant is negative
Which of the following is true about the similarities of Cramer's rule and Gauss-Jordan Method?
- Both Cramer's rule and Gauss- Jordan need non-zero valued element
- All of the answers correct
- Both Cramer's rule and Gauss- Jordan method use augmented matrix Correct
- Both Cramer's rule and Gauss- Jordan method only work for m =E2=89=A0n matrices
Which of the following is true about the systems of linear equation?x + 6y + 3 = 0x + 2y + 4 = 84x + y + z = 4
- using Gauss- Seidel method cannot be applied
- it will not converge
- there are infinite solutions
- the solution will converge Correct
Which of the following statements about algorithm is INCORRECT?
- Algorithms are well-ordered with unambiguous operations
- Algorithms should have explicitly defined set of inputs and outputs
- Algorithms can run for infinitely Correct
- Algorithms must have a unique name
Which of the following statements is true for the function f(x) = -e x + sin x, when 0 is used as an initial value:
- Newton’s method cannot be used Correct
- Newton’s method is convergent
- Newton’s method is divergent
- Newton’s method can be used since the function is “smooth”
While using two sets of points (x0,y0) and (x1,y1) a straight line is formed and could use the slope equation which follows that the first derivative can be approximated using the given values
- True Correct
- False
With the Lagrange form, it is ___________ to pass from one interpolation polynomial to another of degree one greater
- inconvenient Correct
- impossible
- easier
- faster
This course is taught by the mentor:
Master of Arts in Mathematics Education specialization in College Teaching.
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