Numerical Methods - Study Mode

Show All Answers

[#51] A numerical solution of the equation f(x) = x + √x - 3 = 0 can be obtained using Newton-Raphson method. If the starting value is x = 2 for the iteration, the value of X that is to be used in the next step is

(A) 0.306

(B) 0.739

(C) 1.694

(D) 2.306

Correct Answer

(C) 1.694

[#52] To solve the equation 2sin x = x, by Newton Raphson method, the initial guess value is chosen to be x = 2. Consider x in radius only. The value of x (in radius) obtained after one iteration will be closed to

(A) -8.101

(B) 1.901

(C) 2.099

(D) 12.101

Correct Answer

(B) 1.901

[#53] A 2 nd degree polynomial, f(x) has values of 1, 4 and 15 at x = 0, 1 and 2, respectively. The integral $$intlimits_0^2 {{ ext{f}}left( { ext{x}}
ight){ ext{dx}}} $$ xa0 is to be estimated by applying the trapezoidal rule to this data. What is the error (defined as "true value - approximate value") in the estimate?

(A) $$ - frac{4}{3}$$

(B) $$ - frac{2}{3}$$

(C) 0

(D) $$frac{2}{3}$$

Correct Answer

(A) $$ - frac{4}{3}$$

[#54] Starting from x 0 = 1, one step of Newton-Raphson method in solving the equation x 3 + 3x - 7 = 0 gives the next value (x 1 ) as

(A) x 1 = 0.5

(B) x 1 = 1.406

(C) x 1 = 1.5

(D) x 1 = 2

Correct Answer

(C) x 1 = 1.5

[#55] The equation x 3 - x 2 + 4x - 4 = 0 is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, then the next approximation using this method will be

(A) $$frac{2}{3}$$

(B) $$frac{4}{3}$$

(C) 1

(D) $$frac{3}{2}$$

Correct Answer

(B) $$frac{4}{3}$$