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Enter the Taylor series to order x^3:
Enter 0 if you did not do the problem, 1 if the problem is partially correct, and 2 if each step is correct:
Enter the percentage error for N = 50:
Enter the percentage error for N = 100:
Enter the low energy limit for the multiplicity of an Einstein Solid:
Enter an expression for the multiplicity of this macrostate:
Enter the percentage of states that would be explored in 10 billion years:
Enter the value of x that maximizes x^n*exp(-x):
Enter the Taylor approximation of n*ln(x) - x to order y^2. -- Do not include a term of the form O(y^3):
Enter the expression resulting from evaluating this integral:
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