CSC601 Exam. Section C
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Sample question. Iteration with min search
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Problem specification
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Let 

x(1) =  0.3
x(2) = -0.3

x(i) = i + sin(x(i-2)), i = 3, 4, ...

(1) Write a suitable C++ program that generates a sequence
x(1), x(2), ..., x(n), for some n >= 3 which is entered 
by the user from keyboard.           
                                           [8 marks]

(2) Write a suitable addition to the code produced for (1) 
that finds in this sequence the value which is nearest
to some whole number. E.g., for a sequence consisting
of three numbers 3.34, -5.95, 10.06,
the result will be -5.95. The difference between this
value and its nearest whole number (it is 0.05) is
smallest amongst all three values.
                                           [12 marks]

Remarks. 
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To calculate the smallest whole number that is not less than x,
you may call the ceil function with interface:

double ceil(double x)

e.g. ceil(52.31) will return 53.0

To calculate the largest whole number that is not greater than x,
you may call the ceil function with interface:

double floor(double x)

e.g. floor(48.91) will return 48.0

To calculate the absolute value you may call the fabs
function with interface:

double fabs(double x)

e.g.: fabs(3.21) will return 3.21; fabs(-3.14) will return 3.14.        

To calculate sin(x) you may call the sin
with interface:

double sin(double x)

Both functions require inclusion of the math.h file
in your program.