MTH603 Quiz.3 File 5

Question # 1 of 10 ( Start time: 09:32:46 PM ) Total Marks: 1
In Simpson’s rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into an ………… number n of subintervals of equal length.
Select correct option:
Odd
Even  (Correct Answer)
Prime
None of the given choices


Question # 2 of 10 ( Start time: 09:33:13 PM ) Total Marks: 1
At which of the following point the derivatives or slopes the functions f(x) = x – 2 and g(x) = x + 2 may differ?
Select correct option:
differ for every value of ‘x’  (Correct Answer)
does not differ for any value of ‘x’
x = 2
x = -2


Question # 3 of 10 ( Start time: 09:34:18 PM ) Total Marks: 1
Simpson’s rule is a numerical method that approximates the value of a definite integral by using …………polynomials.
Select correct option:
Linear
Quadratic  (Correct Answer)
Cubic
None of the given choices


Question # 4 of 10 ( Start time: 09:34:46 PM ) Total Marks: 1
Which of the following is the Cote’s number (weighting coefficient) for the function: f(x) = x+1 in the interval [0,1]?
Select correct option:
3/2
-3/2
1/2  (Correct Answer)
-1/2


Question # 5 of 10 ( Start time: 09:35:09 PM ) Total Marks: 1
In Simpson’s 3/8 rule, the global error is of ………………
Select correct option:
O(h2)
O(h3)
O(h4)  (Correct Answer)
None of the given choices


Question # 6 of 10 ( Start time: 09:35:34 PM ) Total Marks: 1
Simpson’s 3/8 rule represents the area between the curve y = f(x) in the interval say [a,b] above x-axis by approximating the given curve by the ----------.
Select correct option:
Cubic curve through one point
Cubic curve through two points
Cubic curve through three points  (Correct Answer)
Cubic curve through four points


Question # 7 of 10 ( Start time: 09:35:56 PM ) Total Marks: 1
Zero-th order divided difference is defined as
Select correct option:
y[x0]=x0
y[x0]=y1
y[x0]=y0  (Correct Answer)
None of the given choices


Question # 8 of 10 ( Start time: 09:36:23 PM ) Total Marks: 1
In Simpson’s 1/3 rule, the global error is of ………………
Select correct option:
O(h2)
O(h3)
O(h4)  (Correct Answer)
None of the given choices


Question # 9 of 10 ( Start time: 09:36:50 PM ) Total Marks: 1
To take the derivative of f(x) = 2x in the interval [-3,3], which of the following partition of subintervals will be suitable?
Select correct option:
Equally spaced  (Correct Answer)
Unequally spaced
Union of equally spaced and unequally spaced intervals.
Any arbitrary partition will work


Question # 10 of 10 ( Start time: 09:37:15 PM ) Total Marks: 1
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?
Select correct option:
-pi/80  (Correct Answer)
pi/80
0
1