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Sage Calculus Tutorial -- continuity practice problems

asked 2013-09-27 10:20:25 +0100

Snap gravatar image

Can anyone help me understand how to do some of the practice problems in the sage calculus tutorial? In particular, I'm stuck on problems 5 and on at the bottom of this page

For example, I am not sure how to define 'k'. As it stands, graphing the function in problem 5, sage does not know what to do with the variable 'k', because it is not defined.

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answered 2013-09-27 11:21:30 +0100

calc314 gravatar image

You need to use the definition of continuity, which will involve the limit command, and the solve command to find k.

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answered 2013-09-27 18:41:46 +0100

tmonteil gravatar image

To define the variable k, you can write:

sage: var('k')

Concerning problem 5, Sage does not answer the right result:

sage: solve(limit(cos(x), x=pi/2, dir='-') == limit(sin(x+k), x=pi/2 , dir='+'), k)                    
[k == 1/2*pi]

Indeed, 1/2*pi is one of the solutions, but the solutions are all numbers of the form 1/2*pi+n*pi (where n is an integer). So, you have to be careful with symbolic computations.

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Asked: 2013-09-27 10:20:25 +0100

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Last updated: Sep 27 '13