MTH603 Quiz 3 by VU Topper RM

Richardson extrapolation method is used to improve the rate of convergence of a ………… A. Sequence B.

Series

To evaluate a definite integral of tabular function f(x), piecewise quardratic approximation led to --------- A. Simpson’s Rule B.

Trapezoidal Method

At which of the following points the Minimum value of 2nd derivative of function f(x) = -(2/x) in the interval:[1,4] exits?

1. At x=1
2. At x=2
3. At x=3
4. At x=4

Correct answer: At x=1

In double integration, we keep one variable say x fixed and

A. Reliable the other variable y B.

Varying the other variable y

In Simpson’s 3/8 rule, the global error is of ………………

A. O(h2) B. O(h3)

C. O(h4)

D. None of the given choices

Multistep method does not improves the accuracy of the answer at each step. A. true B.

false

If the area under ‘f(x) = x’ in interval [0,2] is subdivided into two equal sub-intervals of width ‘1’ with right end points, then which of the following will be the Truncation Error provided that I(definite integral) = 2 and approximate sum = 3 ? A. B. C. -1 D.

yn+1=yn+16(K1+2K2+2k3+k4) is known as: A. Taylor’s formula B. Simpson’s formula C. Euler’s formula D.

Runge-Kutta’s formula

Given that dydt=t+y√ with the initial condition y0=1att0=0 find the 2nd term in Taylor series when t=1, y/ =0.2, and h=0.1. A. 0 B. 0.1 C. 0.2

D. 0.3

Given that dydt=y−ty+t with the initial condition y=1,t=0 Using Euler’s method, y ath=0.01; the value of y(0.01)is

A. 1.1

B. 1.2 C. 1.02 D. 1.03

In Trapezoidal rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into n subintervals of equal length using the ………points.

A. N

B. N+1 C. n-1 D. None of the given choices

To evaluate numerically a double integral over a rectangular region bounded by the lines x = a, x =b, y = c, y = d we shall employ either trapezoidal rule or Simpson’s rule, repeatedly with respect to ………variable at a time. A. one B.

two

C. three D. None of the given choice

The double definite integral of a function is called………… A.

Volume under the curve

B. Length of the curve C. Area under the curve D.

If the given tabular function f(x) is approximated by the polynomial ‘P1(x) = x+1’ then which of the following polynomial will approximate the derivative of f(x) ?

1. x
2. x-1
3. 2x
4. 1

Correct answer: 1

Geometrically the definite integral of any continuous function f(x) in the interval [a,b] gives ----------. A.

Area under f(x) on [a,b]

B. Area of Trapezoid with dimension of ‘a’ and ‘b’ C. Volume with dimensions f(x), ‘a’ and ‘b’ D. Length of segment AB on real line

In Simpson’s rule, we can estimate the integral by …………the areas under the parabolic arcs through three successive points. A. B.

Multiplying

C. Adding D. Subtracting

Integration is a ………………process.