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Suppose O can produce corn for $1 per bushel and wheat for $6 per bushel while S can produce corn for $2 per bushel and wheat for $4 per bushel. O has an absolute and comparative advantage in corn while S has an absolute and comparative advantage in wheat.

An increase in consumer incomes will lead to increases in the prices of all grocery store items. Please explain why this statement is true, false, or uncertain.

Q. 4 (a) If ,1xfxx show that .01"f (3) (b) Find the nth derivative of .22axx (3) (c) If cos ,nxlogbynthen show that 02122122nnnynxynyx (4

A binary encoded signal with a bit-rate of Rb = 56 kbps is encoded using Uni-polar NRZ baseband encoding and then modulated using binary PSK (BPSK). What is the bandwidth required to transmit this modulated signal?

A 224 kHz

B 56 kHz

C 112 kHz

D 28 kHz

E 14 kHz

Please show working out if you can ?

3 (a) Show that f, given by 0x,00x,x1sinxf(x) is continuous at each point of R. (4) (b) Check whether the function f: RR given by ,xxxfis one one onto. Give reasons for your answers. (3) (c) Find .5limxx Also, show this graphically

Q. 1 Which of the following statements are true? Give reasons for you answer. (This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. For instance, to show that {1, Padma, blue} is a set’ is true, you need to say that this is true because it is well defined collection of 3 objectives.) (i) The domain of the function f given by }.{1\Ris1x2xf(x)22 (ii) Any curve with portions in the first and second quadrants is symmetric about y-axis. (iii) 121lim1limxxx does not exist. (iv) An ever function cannot be monotonic. (v) The curve )1(1)4(22xy has no asymptote parallel to axes. (vi) A function f, defined by f(x) = x sin x + cos x, is decreasing in .π/2o, (vii) If 11,)(odxxf then f must be an even function. (viii) .coscossin22xxdttdxdxx (ix) 1x2f(x)bygiven:fRRis differentiable on R. (x) The slope of the tangent of the curve 22xxy at the origin is 0. (20

c) Find the angle between the x-axis and the tangent to the hyperbola xy = 9 at (3, 3).

b) Evaluate (i) 1383777limxxx (ii) 2

1. Write a program that consists of a while-loop that (each time around the loop) reads two ints and then prints them. Exit the program when a terminating '|' is entered.

2. change the program to write out "the smaller value is:" followed by the smaller of the numbers and "the larger value is:" followed by the larger value.

A book binder has one printing press, one binding machine and manuscripts of seven

different books. The time required for performing printing and binding operations for

different printing and binding operations for different books are shown below:

Book 1 2 3 4 5 6 7

Printing Time 20 90 80 20 120 15 65

(Days)

Binding Time 25 60 75 30 90 35 50

(Days)

Find the optimum sequence of processing of the jobs that minimises the total time required.

Also compute the optimal time required.