What annual payment is required to pay off a four-year, $30,000 loan if the interest rate being charged is 6 percent EAR? What would the monthly payments be for the same loan assuming the same interest rate? 

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One solution to the Bessel equation of (nonnegative) integer order N x²y" + xy' + (x² - N²) y = 0 is y(x) = JN(x) = k=0 (-1)k k!(N + k)! (²) ² J (0, x, m) (a) Write the first three terms of Jo(x). (b) Let J (0, x, m) denote the mth partial sum x\ 2k+N m (-1)k 2k (k!)² Plot J (0, x, 4) and use your plot to approximate the first positive zero of Jo(x). Compare your value against a tabulated value or one generated by a computer algebra system. (c) Plot Jo(x) and J (0, x, 4) on the same axes over the interval [0, 2]. How well do they compare? (d) If your system has built-in Bessel functions, plot Jo (x) and J(0, x, m) on the same axes over the interval [0, 10] for various values of m. What is the smallest value of m that gives an accurate ap- proximation to the first three positive zeros of Jo(x)? One solution to the Bessel equation of (nonnegative) integer order N x²y" + xy' + (x² - N²) y = 0 is y(x) = JN(x) = k=0 (-1)k k!(N + k)! (²) ² J (0, x, m) (a) Write the first three terms of Jo(x). (b) Let J (0, x, m) denote the mth partial sum x\ 2k+N m (-1)k 2k (k!)² Plot J (0, x, 4) and use your plot to approximate the first positive zero of Jo(x). Compare your value against a tabulated value or one generated by a computer algebra system. (c) Plot Jo(x) and J (0, x, 4) on the same axes over the interval [0, 2]. How well do they compare? (d) If your system has built-in Bessel functions, plot Jo (x) and J(0, x, m) on the same axes over the interval [0, 10] for various values of m. What is the smallest value of m that gives an accurate ap- proximation to the first three positive zeros of Jo(x)?

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