1 Objective Questions

     2 -------------------

     3 

     4 .. A mininum of 8 questions here (along with answers)

     5 

     6 1. How do you define a name 'y' as a symbol?

     7 

     8 

     9    Answer: var('y')

    10 

    11 2. List out some constants pre-defined in sage?

    12 

    13    Answer: pi, e ,euler_gamma

    14 

    15 3. List the functions for differentiation and integration in sage?

    16 

    17    Answer: diff and integral

    18 

    19 4. Get the value of pi upto precision 5 digits using sage?

    20 

    21    Answer: n(pi,5)

    22 

    23 5.  Find third order differential of function.

    24 

    25     f(x)=sin(x^2)+exp(x^3)

    26 

    27     Answer: diff(f(x),x,3) 

    28 

    29 6. What is the function to find factors of an expression?

    30 

    31    Answer: factor

    32 

    33 7. What is syntax for simplifying a function f?

    34 

    35    Answer f.simplify_full()

    36 

    37 8. Find the solution for x between pi/2 to pi for the given equation?

    38    

    39    sin(x)==cos(x^3)+exp(x^4)

    40    find_root(sin(x)==cos(x^3)+exp(x^4),pi/2,pi)

    41 

    42 9. Create a simple two dimensional matrix with two symbolic variables?

    43 

    44    var('a,b')

    45    A=matrix([[a,1],[2,b]])

    46 

    47 Larger Questions

    48 ----------------

    49 

    50 .. A minimum of 2 questions here (along with answers)

    51 

    52 1.Find the points of intersection of the circles

    53 

    54  x^2 + y^2 - 4x = 1 

    55  x^2 + y^2 - 2y = 9  

    56 

    57 2. Integrate the function 

    58 

    59 x^2*cos(x)

    60 

    61 between 1 to 3.