CROSSMATHS Puzzle

As usual this puzzle is contributed by Mr Thomas Masiwa, and a prize of $100 is offered for the first correct solution to be opened after 30th April 2001. In this puzzle the solutions are in numbers. Each solution is a three digit number. Decimal points are ignored but if the solution is not an integer, it should be given correct to that number of decimal places that yields a three digit number not starting with 0.

ACROSS
 1. f(1) given that f(x) = f^¢(x) (function is equal to its derivative at every point), and f(0) = 1.
 3. Ten times the sine of Ö2 radians.
 5. Find y such that y is a perfect square and so is [(y - 1)/2].
 6.  x such that x^1/3 = 30 ¸3!.
 8.  X such that X = 2m² + 32, where m is an integer.
10.  Square of a prime integer.
12.  The product: 3!(3⁴ + 3!).
14.  lim_{n ® ¥} (1 + [1/n] )⁶ⁿ.
15.  Ten times the sine of f(1) in 1 across.
16.  The seventh root of 1,6.

DOWN
 1.  e^p.
 2.  p^e.
 3.  3³(3³ + 3² + 3⁰).
 4.  The product of the area of a circle of radius 1 unit and f(1) in 1 across.
 7.  ( (2000)⁰ + (2001)⁰ )⁸.
 9.  The positive root of r² - r - 1 = 0. (Golden Ratio).
10.  The area of a circle of radius 1 unit.
11.  The length of the diagonal of a one square unit regular quadrilateral.
12.  (2⁶ - 5)3².
13.  A Fermat prime, that is a number of the form 2^2x + 1.

P.S. The centre number is such that the sum of the sums of the numbers appearing on the diagonals is two more than a perfect square.