Minimum capacity rate ratio of a heat exchanger

1. The problem statement, all variables and given/known data
Here is the question:

I am confused about the solution. In the solution they found that the minimum capacity rate ratio R = C_min/C_max was zero. This is because of the term I circled in the red which I do not understand why it goes towards infinity.

Here is the solution:

Could someone please explain why that term goes to infinity?

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