
Use the taylor command to find the fifthorder Maclaurin polynomial for y = tan^{1} x.

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.

Use the taylor( command to find the secondorder Taylor polynomial centered at 2 for y = e^{x}.

Use the taylor( command to find the fourthorder Maclaurin polynomial for y = e^{x2}. Take the derivative of this polynomial. Use these results to predict the thirdorder Maclaurin polynomial for y = 2xe^{x2}. Verify your prediction by using the taylor( command to find the thirdorder Maclaurin polynomial for y = 2xe^{x2}.

Use the taylor( command to find the fourthorder Maclaurin polynomial for y = e^{x2}. Take the integral of this polynomial and use the result to predict the fifthorder Maclaurin polynomial for
.
Click here to check your answers.
