Unformatted text preview: e borderlin e of two bars, then f n x is the midpoint of the base of the leftmost of those two bars.
a. Show that for all x
b. Let g(x) = (e 2x
E g D2 n , lim f n x x. n 3 . Show that 2n g fn x p n x x. a. For each n , the width of the bars of H n are 2
an d the span of H n is 2n 1 2n , 2n 2n ,
1 2 n . Therefore, a fixed x
must eventually lie in the span of H n ,
an d the value of f n x then con verges to xsince the widths of the bars decreases.
b. We first evaluate the left hand side, E g D2 n 2n...
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This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.
- Spring '08