test-numerical

Use the Bisection method on f(x) = x ^ 3 - cos x + 1 which of the follwing interval that f(x) changes sign?

• f(x) changes sign on the interval - 0.9 <= x <= - 0.8

• f(x) changes sign on the interval 0 <= x <= 1

• f(x) changes sign on the interval - 0.5 <= x <= 0, 4

• f(x) changes sign on the interval - 0.4 <= x <= - 0.3

Find the root of x^4-x-10 = 0 approximately upto 5 iterations using Bisection Method on the interval [1.5, 2]:

• 1.88

• 1.86

• 1.68

• 1.66

A function f(x) is given as e^(-x)* (x^2+5x+2) + 1 = 0 on the interval [-1,0]. Find the relative error upto 6 iterations

• 2.7227%

• 2.7327%

• 2.7127%

• 2.7027%

Using Bisection method find the root of cos(x) - x*e^x =0 with a = 0 and b = 1, correct to 5 decimal places

• 0.57612

• 0.56712

• 0.57713

• 0.56812

Numerical method is an approach for solving complex mathematical problem using

• complex arithmetic operations

• simple algebraic operations

• simple arithmetic operations

What is continuous function?

• A function which plots on straight lines

• All of these

• A function which for small changes in the argument outputs also small changes of the result

• A function which for small changes in the argument outputs big changes of the results

For any given system of linear equations, what are the possible solutions?

• No solution

• All of these

• Unique solution

• Infinite many solutions

If f(x) is continuous in the interval [a, b] and if f(a) and f(b) are of opposite signs then the equation f(x)=0, there is (are)

• One root

• Two roots

• At least one root

• No root

Errors may occur in performing numerical computation on the computer due to

• Rounding errors

• Power fluctuation

• Operator fatigue

• All of these

Which of the following statements applied to the Bisection method used for finding roots of functions?

• Guaranteed to work for all continuous functions b. Convergers within a few iterations

• Convergers within a few iterations

• Is faster than the Newton-Raphson method

• Required that there be no error in determining the sign of the function