MTH603 Quiz 4 by VU Topper RM

Given that with the initial condition Using Modified Euler’s method, for the range , h = 0.1 is

A. 1.2

B. 1.1 C. 2.1 D. 1.0

Which of the following is the Global Error for Simpson’s 3/8 Rule while integrating ‘f(x) = Cosx’ in the interval of [0,pi] of equally spaced subinterval of width ‘h =pi/6’ and intermediate point x = pi/2?

1. -pi/80
2. 0
3. pi/80
4. 1

Correct answer: pi/80

If , and h= 0.2. Then, of Runge-Kutta method is: A. 0.1 B. 0.4

C. 0.2

D. 0.3

The single definite integral of a function is called ……… A. Volume of the curve

B. Area under the curve

C. Length of the curve D. None of the given choices

when t=1, y/ =1.2, and h=0.1.

A. 1.2

B. 1.4 C. 1.5 D. 1.3 Given that with the initial condition find the 2nd term of Taylor series

A. 0 B. 0.3 C. 0.1

D. 0

----------- difference is a symmetric function of its arguments. A. Forward B. Backward C. None

D. Divided

What will be the value of first order divided difference f[1,5]for the following data x:0 1 5 y:2 1 5

A. 1

B. 3 C. 2 D. 0

A. 8 B. 6

C. 2

D. 4

If y(x) is approximated by a polynomial of degree n then the error is given by Pn(x) A. ε(x) = y(x) ÷ Pn(x) B. ε(x) = y(x) + Pn(x) C. ε(x) = y(x) × Pn(x)

D. ε(x) = y(x) − Pn(x)

In Lagrange’s interpolation, for n values of y corresponding to n values of x, we can represent the function f (x) by a polynomial of degree A. n

B. n-1

C. n+1 D. n+2

A. 0 B. 1

C. 2

D. -2

If there are (n+2) values of y corresponding to (n+2) values of x, then we can represent the function f(x) by a polynomial of degree A. n-1

B. n+1

C. n+2 D. n

Given the following data x:1 2 7 11 y:6 10 13 37 Which formula is useful in finding the interpolating polynomial?

1. Newton’s backward difference interpolation formula
2. Lagrange’s interpolation formula
3. Newton’s forward difference interpolation formula
4. None

Correct answer: Newton’s forward difference interpolation formula

Given the following data x:4 5 7 10 y:46 102 294 346 Value of 1st order divided difference f[5 , 7] is A. 94