mmaexercises2soln

# mmaexercises2soln - 2011 Steven Tschantz Mathematica...

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© 2011 - Steven Tschantz Mathematica exercises part 2 Steven Tschantz 1/18/11 Exercises Complete the following exercises, save your results, and email your final version to [email protected] 1. How many digits are there in the decimal form of the integer 100! (factorial)? You can easily calculate 100! but it would be tedious to count the digits. An n -digit integer x is an integer with 10 n - 1 £ x < 10 n . So the number of digits of x is related to common log (log base 10) of x . In Mathematica, Log is the natural log, but there is also a form that calculates log to other bases (look it up). In[1]:= Floor @ Log @ 10,100 ! DD + 1 Out[1]= 158 100! has 158 digits In[2]:= Length @ IntegerDigits @ 100 ! DD Out[2]= 158 2. Apply the method of undetermined coefficients to find a parabola y=a*x^2+b*x+c through the points (0,1), (1,6), (3,4). In terms of the unknown coefficients, write down the three equations defining when the parabola contains the three given points and solve for the coefficients. See the example in the posted notebook on Mathematica foundations.

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