diff -r 88a01948450d -r d33698326409 using-sage/questions.rst --- a/using-sage/questions.rst Wed Nov 17 23:24:57 2010 +0530 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,99 +0,0 @@ -Objective ---------- - -1. How do you find the limit of the function ``x/sin(x)`` as ``x`` tends to - ``0`` from the negative side. - - Answer: lim(x/sin(x), x=0, dir="below") - -#. Find the third differential of the function ``exp(sin(x)*cos(x^2))`` - - Answer: diff(exp(sin(x)*cos(x^2), x, 3) - -#. Solve the system of linear equations:: - - x-2y+3z = 7 - 2x+3y-z = 5 - x+2y+4z = 9 - - Answer:: - - A = Matrix([[1, -2, 3], - [2, 3, -1], - [1, 2, 4]]) - - b = vector([7, 5, 9]) - - solve_right(A, b) - -#. How do you get the factorized form of ``x^4 - 4x^2 + x^3 + 2x + 7`` - - Answer:: - - factor( x^4 + x^3 - 4*x^2 + 2*x + 7 ) - -#. list all the primes between 2009 and 2900 - - Answer: prime_range(2009, 2901) - -#. Which function is used to check primality - - a. isPrime - #. isprime - #. is_prime - #. prime - - Answer: is_prime - -#. How do you list all the combinations of ``[1, 2, 3, 4]`` - - - Answer:: - - c1 = Combinations([1, 2, 3, 4]) - c1.list() - -#. How do you list all the permutations of ``[1, 3, 2, 3]`` - - Answer:: - - p1 = Permutations([1, 3, 2, 3]) - p2.list() - - -Programming ------------ - -1. Obtain the sum of primes between 1 million and 2 million. - - Answer:: - - prime_sum = 0 - for i in range(1000001, 2000000, 2): - if is_prime(i): - prime_sum += i - - prime_sum - - OR - :: - - sum(prime_range(1000000, 2000000)) - -2. ``graphs.WorldMap()`` gives the world map in the form of a - graph. :: - - G = graphs.WorldMap() - G.vertices() - - - Suppose, I wish to go from India to France by Road, find out the - least number of Visas that I'll have to obtain. - - Answer:: - - G.distance("India", "France") - - - -