Question

1. (Based on problem 39, Section 8.6 from Stewart's 2nd Edition of Essential Calculus) Let C.T n=1 (a) Define this function in Mathematica using f-Sum[x^n/n*2,fn,1,10)]. Then enter f into Mathematica to see the power series expansion (b) Find f', and f" of the power series expansion using the D command (c) Write the derivatives as power series in SUMMATION NOTATION, i.e. use sigma notation. Again you can use the D command to get the derivative. For example, to find f' simply use the command D[x^n/n*2,x]. Then rewrite in summation notation. Be careful of where you start the index of the summation if the n 1 term is a constant then it's derivative is 0 and we must start at n 2 (d) Find the intervals of convergence for f, f', and f" using the command Sum Convergence. If you're unsure of the endpoints plug them in for x and use the command SumConvergence to check (e) Suppose you were going to find the interval of convergence by hand. State the Test of Convergence you would use to find the endpoints of the interval of convergence for each of f, f', and f".

Answer 1

Wolfram Mathematica 9.0-(Untitled-1 *] File Edit Insert Fomat Cell Graphs ation Palettes Window Help Untitled-1 "Define the function" n5- Sum,[n, 1, 10) "enter f for power serics cxpansion" n4 f[x] 4 916 25 36 49 681 100 "derivative of f using D command" 2 3 45 678 9 10 "double derivative of f using D command" Out 10 9 10 In[13] "Summation notation of first derivative" Out13- Summation notation of first derivative Out[141- "Summation notation of second derivative" 100% 02:56 ?ENG 25-04-2019 O Type here to search

Wolfram Mathematica 9.0-(Untitled-1 *] File Edit Insert Fomat Cell Graphs ation Palettes Window Help Untitled-1 , "Summation notation of second derivative (n-1) x-2) Out[ 15ㅑ "Sum convergance of f[x]" Int18]:: SumConvergence |ー, n Sam convergance of x] x0-1) "Sum convergance of f [x]" (n 1) x(-2) In|20] Abs [x] 1 100% ▲ 02:56 O Type here to search ENG 25-04-2019 ^