Algorithms Answers

x sin x d_ sin x = cos x

dx

0.30 0.29552 0.95534

0.32 0.31457 0.94924

0.35 0.34290 0.93937

0.50 0.47943 0.87758

(1.1) Construct a Lagrange interpolating polynomial that interpolates the function at all the points. Use the Lagrange polynomial to approximate sin 0.33.

(1.2) Use all the points to construct a Newton’s divided difference interpolating polynomial and use it to approximate sin 0.33.

(1.3) Use the first three data points and five-decimal digit arithmetic with rounding to construct a cubic spline S with boundary conditions.

S 0 (x0) = f 0 (x0) and S 0 (xn) = f 0 (xn) 

which forces the slopes of the spline to assume certain values at the two boundaries. Use the spline to approximate sin 0.33.

(1.4) Determine and compare the errors in the approximation in (1.1)-(1.3)

(1.5) Use the spline constructed in (1.3) to approximate cos 0.34

Consider the following data: x sin x d dx sin x = cos x 0.30 0.29552 0.95534 0.32 0.31457 0.94924 0.35 0.34290 0.93937 0.50 0.47943 0.87758

(1.1) Construct a Lagrange interpolating polynomial that interpolates the function at all the points. Use the Lagrange polynomial to approximate sin 0.33.

(1.2) Use all the points to construct a Newton’s divided difference interpolating polynomial and use it to approximate sin 0.33.

(1.3) Use the first three data points and five-decimal digit arithmetic with rounding to construct a cubic spline S with boundary conditions S 0 (x0) = f 0 (x0) and S 0 (xn) = f 0 (xn) which forces the slopes of the spline to assume certain values at the two boundaries. Use the spline to approximate sin 0.33.

Q1. Explain strategies and options for distributed database design.

Q2. Explain advantages and risks of distributed databases.

Q3. Discuss relative advantages of synchronous and asynchronous data replication and partitioning.

Q4. Describe salient characteristics of distributed database environments.

Question 1:

Distinguish between analogue and parametric estimation in cost management

Question 2:

Examine the importance of quality auditing in project management.

A B C D E

Now perform the following operations on the Dequeue

(a) Add F on the left

(b) Add G on the right

(c) Add H on the right

(d) Delete two letters from the left

(e) Add I on the right

(f) Add J on the left

(g) Delete two letters from right

(2) Let X denote a random variable model with density function given by

Compute the 

(i) expected value                   

(ii) standard deviation

1)A random variable is defined as 

  (a)Construct the Probability distribution function of X.

  (b) Compute;

     (i) the standard deviation of X            

  (ii) E                      

    (iii)Var

Q(3)It is known that only 60% of a defected computer can be   

   repaired. A sample of 15 computers is selected randomly,   

   find the probability that;

 (i) None can be repaired  ​        

 (ii) 5 or less can be repaired ​     

(iii) At least 3 computers can be repaired. 

Q(2)A random variable is defined as Construct the probability distribution function

of X and find the standard deviation of X.