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You can use Wolfram Alpha to get exact solutions for different k, although the results are expressed in not-so-good functions

This allows to build smooth plots:

http://storage4.static.itmages.ru/i/11/0220/h_1298189475_0effdae27f.png http://storage5.static.itmages.ru/i/11/0220/h_1298189539_2043dbc994.png

(both plots are for k=5)

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You can use Wolfram Alpha to get exact solutions for different k, although the results are expressed in not-so-good functions