1. Use the taylor command to find the fifth-order Maclaurin polynomial for y = tan^-1 x.
2. Graph y = tan^-1 x with a "thick" graphing style. In the same window graph the 5th-, 9th- and 13th- order Maclaurin polynomials for this function. Estimate the interval of convergence for the series based on your graph.
3. Use the taylor( command to find the second-order Taylor polynomial centered at 2 for y = e^x.
4. Use the taylor( command to find the fourth-order Maclaurin polynomial for y = e^x2. Take the derivative of this polynomial. Use these results to predict the third-order Maclaurin polynomial for y = 2xe^x2. Verify your prediction by using the taylor( command to find the third-order Maclaurin polynomial for y = 2xe^x2.
5. Use the taylor( command to find the fourth-order Maclaurin polynomial for y = e^x2. Take the integral of this polynomial and use the result to predict the fifth-order Maclaurin polynomial for .

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