18.05 Lecture Notes - Lecture 3: Mit Opencourseware

3. (20 polnts) Taylor/Maclaurin Polynomlals. Consider the function(x)-e . (1S pts) Find 34 order polynomial P(x) to approximate f(x) at o (a b. (5 polnts) Approximate f(0.1) using P(x).

Consider the initial value problem:y2+1 Using Euler's method: ynynthy +1n with step-size h 0.05, obtain an approximate solution to the initial value problem at x-0.1 Maintain at least eight decimal digit accuracy throughout all calculations. You may express your answer as a five decimal digit number, for example 6.27181 YOU DO NOT HAVE TO ROUND YOUR FINAL ESTIMATE , 4y2+1 th, Estimate at x- 0.1 is