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1 Objective |
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2 --------- |
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3 |
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4 1. How do you find the limit of the function ``x/sin(x)`` as ``x`` tends to |
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5 ``0`` from the negative side. |
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6 |
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7 Answer: lim(x/sin(x), x=0, dir="below") |
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8 |
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9 #. Find the third differential of the function ``exp(sin(x)*cos(x^2))`` |
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10 |
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11 Answer: diff(exp(sin(x)*cos(x^2), x, 3) |
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12 |
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13 #. Solve the system of linear equations:: |
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14 |
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15 x-2y+3z = 7 |
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16 2x+3y-z = 5 |
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17 x+2y+4z = 9 |
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18 |
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19 Answer:: |
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20 |
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21 A = Matrix([[1, -2, 3], |
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22 [2, 3, -1], |
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23 [1, 2, 4]]) |
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24 |
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25 b = vector([7, 5, 9]) |
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26 |
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27 solve_right(A, b) |
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28 |
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29 #. How do you get the factorized form of ``x^4 - 4x^2 + x^3 + 2x + 7`` |
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30 |
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31 Answer:: |
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32 |
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33 factor( x^4 + x^3 - 4*x^2 + 2*x + 7 ) |
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34 |
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35 #. list all the primes between 2009 and 2900 |
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36 |
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37 Answer: prime_range(2009, 2901) |
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38 |
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39 #. Which function is used to check primality |
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40 |
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41 a. isPrime |
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42 #. isprime |
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43 #. is_prime |
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44 #. prime |
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45 |
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46 Answer: is_prime |
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47 |
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48 #. How do you list all the combinations of ``[1, 2, 3, 4]`` |
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49 |
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50 |
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51 Answer:: |
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52 |
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53 c1 = Combinations([1, 2, 3, 4]) |
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54 c1.list() |
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55 |
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56 #. How do you list all the permutations of ``[1, 3, 2, 3]`` |
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57 |
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58 Answer:: |
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59 |
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60 p1 = Permutations([1, 3, 2, 3]) |
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61 p2.list() |
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62 |
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63 |
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64 Programming |
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65 ----------- |
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66 |
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67 1. Obtain the sum of primes between 1 million and 2 million. |
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68 |
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69 Answer:: |
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70 |
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71 prime_sum = 0 |
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72 for i in range(1000001, 2000000, 2): |
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73 if is_prime(i): |
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74 prime_sum += i |
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75 |
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76 prime_sum |
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77 |
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78 OR |
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79 :: |
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80 |
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81 sum(prime_range(1000000, 2000000)) |
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82 |
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83 2. ``graphs.WorldMap()`` gives the world map in the form of a |
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84 graph. :: |
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85 |
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86 G = graphs.WorldMap() |
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87 G.vertices() |
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88 |
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89 |
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90 Suppose, I wish to go from India to France by Road, find out the |
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91 least number of Visas that I'll have to obtain. |
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92 |
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93 Answer:: |
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94 |
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95 G.distance("India", "France") |
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96 |
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97 |
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98 |
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99 |