getting-started-with-symbolics/questions.rst
author anand
Thu, 11 Nov 2010 00:03:57 +0530
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Objective Questions
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.. A mininum of 8 questions here (along with answers)
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1. How do you define a name 'y' as a symbol?
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   Answer: var('y')
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2. List out some constants pre-defined in sage?
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   Answer: pi, e ,euler_gamma
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3. List the functions for differentiation and integration in sage?
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   Answer: diff and integral
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4. Get the value of pi upto precision 5 digits using sage?
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   Answer: n(pi,5)
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5.  Find third order differential of function.
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    f(x)=sin(x^2)+exp(x^3)
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    Answer: diff(f(x),x,3) 
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6. What is the function to find factors of an expression?
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   Answer: factor
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7. What is syntax for simplifying a function f?
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   Answer f.simplify_full()
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8. Find the solution for x between pi/2 to pi for the given equation?
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   sin(x)==cos(x^3)+exp(x^4)
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   find_root(sin(x)==cos(x^3)+exp(x^4),pi/2,pi)
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9. Create a simple two dimensional matrix with two symbolic variables?
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   var('a,b')
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   A=matrix([[a,1],[2,b]])
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Larger Questions
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.. A minimum of 2 questions here (along with answers)
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1.Find the points of intersection of the circles
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 x^2 + y^2 - 4x = 1 
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 x^2 + y^2 - 2y = 9  
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2. Integrate the function 
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x^2*cos(x)
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between 1 to 3.