<jupyter_start><jupyter_text>Homework 3 <NAME> 2/29/16  LoanCalculates the amount of a loan left over as well as the payment made that month for a given loan amount, interest rate, and number of months.<jupyter_code>p1.loan_calculator(1000, 12, 5)[0][0] #First month's remaining loan
p1.loan_calculator(1000, 12, 5)[0][-1] #Last month's remaining loan
p1.loan_calculator(1000, 12, 5)[1][1] #First payments's interest
p1.loan_calculator(1000, 12, 5)[1][-1] #Last payment's interest<jupyter_output><empty_output><jupyter_text>root_finder_examplesFinds the numerical roots for a function based on three methods, then outputs a table of thosex-values for the root as well as the relative error for the approximation.<jupyter_code>p2.run(sinh, cosh, -1, 1, 1, 1.1)<jupyter_output><empty_output><jupyter_text>arclengthCalculates the arclength of a function with the classic formula but taken over discrete integration. Here we see the final integral of an erg function over the interval -2 to 2.<jupyter_code>print p3.arclength(p3.part_c, -2, 2, 100)[-1]<jupyter_output>4.04857187118<jupyter_text>sin_Taylor_series_diffeqTakes the Taylor Series expansion for sin at a given point x up to the given number of nth term. Here we show a table which compares performance for several different x and n values.<jupyter_code>p4.table()<jupyter_output>X-Value         N-Value               Approx                Error

       0.200000               2             0.198667            -0.000003

       0.200000               4             0.198669            -0.000000

       0.200000              10             0.198669             0.000000

       1.570000               2             0.925018            -0.074982

       1.570000               4             0.999843            -0.000156

       1.570000              10             1.000000             0.000000

       3.140000               2            -2.019857            -2.021450

       3.140000               4            -0.073292            -0.074885

       3.140000              10             0.001593            -0.000000
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