As in Exercises 3.6, for some problems you will find it essential to have a calculator or computer available.† For Problems 1–17, note whether or not is bounded.
The Taylor method of order 2 can be used to approximate the solution to the initial value problem
at x = 1. Show that the approximation yn obtained by using the Taylor method of order 2 with the step size 1/n is given by the formula
The solution to the initial value problem is y = ex, so yn is an approximation to the constant e.
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