By decinnial census, the population of a town was given below

Year (x) : 1971 1981 1991 2001 2011

Population (y): 112 132 158 189 226 (in thousands)

(i) Using Stirling's central difference formula, estimate the population for the year 2006

(ii) Using Newton's forward formula, estimate the population for the year 1992.

(iii) Using Newton's backward formula, estimate the population for the year 1980.

For the following data develop difference table and find forward differences and backward differences

Express A³fi as a central difference.

Express A³f, as a backward difference.

Explain what is the role of interpolation in solving numerical problems?

Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method

Determine the smallest roots of the following equation:

 to three significant digits using

Perform four iterations (rounded to four decimal places) using

(i) Jacobi Method and

(ii) Gauss-Seidel method,

for the following system of equations

. The exact solution is (1, 2, 3)^T. Which method gives better approximation to the exact solution?

Solve the system of equations

using Gauss elimination method with partial pivoting.

Obtain Approximate the value of (3.7)^-1 using first three terms of Taylor's series expansion.

Calculate a bound for the truncation error in approximating

 where  and (fact n) denotes factorial of n

Find out to how many decimal places the value 22/7 is accurate as an approximation of 3.14159265, where the latter is value of, calculated up to 8 places after decimal?

Explain with suitable example that in computer arithmatics (i.e., numbers represented in computer, with +, -, , / as implemented in a computer) the multiplication operation() may not be distributive over plus (+), i.e.  may not be true for some computer numbers a, b and c

Explain each of the following concepts, along with at least one suitable example for each: (i) Fixed-point number representation (ii) round-off error (iii) representation of zero as floating point number (iv) significant digits in a decimal number representation (v) normalized representation of a floating point number (vi) overflow

Write an e-mail to your friend sharing your reasons to join a particular company. Give appropriate reasons for your choice and how that would be meaningful for the society large.

Discuss various kinds of communication with suitable examples. Discuss kinds of communication and their significance.

Fill in the blanks with suitable articles (a/an, the or no article)

1. I saw ____________ beautiful sunset over the ocean last night.

2. Can you pass me _____________ pen on the desk?

3. My friend is ___________ engineer who works for _____________ large tech company.

4. I need to buy __________ new pair of shoes for ____________ my job interview.

5. ___________ Eiffel Tower is ___________ iconic landmark in Paris.

6. She is ___________ artist who paints __________ most stunning landscapes.

7. I would like to visit _____________ Grand Canyon during ___________ summer.

8. My sister is ___________ accountant, and she works at ____________ local firm.

9. ____________ apple a day keeps ___________ doctor away.

10. I'm going to _____________ park to walk _____________ dog.

Complete the following sentences by putting the verbs in the Simple Past, Past Perfect or Past Continuous Tense:

1. By the time I __________ (arrive) at the party, most of the guests ________ (leave).

2. While I __________  (study) for my exam, my friend _________ (call) to invite me to the movies.

3. The team _________ (win) the championship after they _________ (work) hard all season.

4. I _________ (walk) to the park when it ________ (start) to rain.

5. By the end of the week, I __________ (finish) all my chores and _______(relax) on the weekend.

6. The children _________ (play) in the park when their mother __________ (come) to pick them up.

7. After the concert, the band _________ (greet) their fans and _______(sign) autographs.

8. I _________ (watch) a movie when my roommate ___________ for dinner. (come) home and ____________ (ask) me to join them

9. The teacher ___________ (explain) the lesson while the students _________(take) notes.

10. By the time I __________(graduate), I ____________ (apply) to several jobs and ____________ (receive) a few offers.

Change the following into passive voice:

1. The chef prepared a delicious meal for the guests.

2. The teacher will assign a project to the students next week.

3. The construction workers are building a new bridg

4. The police arrested the suspect last night.

5. The company will launch a new product next month.

Complete the sentences with the comparative or superlative form of the adjective/adverb.

1. This year's vacation was ___________ (good) than last year's.

2. She is the ___________ (intelligent) student in the class.

3. The weather is ___________ (warm) today than it was yesterday.

4. My sister runs __________ (fast) than I do.

5. This is the ___________ (expensive) restaurant in the city.