For a non negative whole number n, let the function fn be given by (picture). where n!= 1*2...n, with the convention that 0!=1, so that f0(x)=1, f1(x)=1+x and so on. A: Show by induction that for all non negative whole numbers n, f2n(x) is a positive number for all real numbers x. B: By using the answer from A, how can we conclude that f9: R(real numbers)-->R(real numbers) has an inverted function ? Does f10 have an inverted function? C: Given n>=0 explain that limx->0 fn(x)/ex=0
For a non negative whole number n, let the function fn be given by (picture). where n!= 1*2...n, with the convention that 0!=1, so that f0(x)=1, f1(x)=1+x and so on. A: Show by induction that for all non negative whole numbers n, f2n(x) is a positive number for all real numbers x. B: By using the answer from A, how can we conclude that f9: R(real numbers)-->R(real numbers) has an inverted function ? Does f10 have an inverted function? C: Given n>=0 explain that limx->0 fn(x)/ex=0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For a non negative whole number n, let the function fn be given by (picture).
where n!= 1*2...n, with the convention that 0!=1, so that f0(x)=1, f1(x)=1+x and so on.
A: Show by induction that for all non negative whole numbers n, f2n(x) is a positive number for all real numbers x.
B: By using the answer from A, how can we conclude that f9: R(real numbers)-->R(real numbers) has an inverted function ? Does f10 have an inverted function?
C: Given n>=0 explain that limx->0 fn(x)/ex=0
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