Webwork question

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I don't quite understand what this problem is asking us to take the limit
of.  After (polar) integration, my resulting expression is the sum of two
trigonometric functions, with psi as their argument, a constant term, and a
term that is the product of c and psi.  I'm not sure how to go about taking

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First of all, a point of information and a request.  I am getting webwork questions from you guys without mention or identification of the question in discussion.  I'm not sure if this is a webwork problem or because you guys are not sending feedback from the question itself.  Please make sure that your webwork questions originate from the specific problem *AND* that your feedback mentions the webwork question number.  Otherwise I may not have time to search through all of the problems to answer your question.  Now, I guess that you are referring to the this webwork problem:

The situation is that your relative has baked a lopsided cake and you would like to slice it in half so that each half has an equal volume of cake. If c=10 the cake is very lopsided: the cake comes to a thin edge at one point and a thick edge at the opposite side.

On the other hand, when the c=30 the cake is relatively more even.

When c is small, given that your first cut is along the positive x-axis and that the peak of the cake is somewhere between the positive x-axis and the positive y-axis you will need to choose your second cut somewhere between before the negative x axis in order to split the cake fairly.   As c--> infinity, I guess that the position of the cut will tend to the negative x axis--but this is what you have to prove.