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a. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x in an open interval (-c, c), then a, = b, for every n. (Hint: Let f(x) = E0a,x" = show that a, and b, both equal f®(0)/(n!).) b. Show that if Eo a,x" = 0 for all x in an open interval (-c, c) then a,n E=ob,x". Differentiate term by term to 0 for every n.

a. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x in an open interval (-c, c), then a, = b, for every n. (Hint: Let f(x) = E0a,x" = show that a, and b, both equal f®(0)/(n!).) b. Show that if Eo a,x" = 0 for all x in an open interval (-c, c) then a,n E=ob,x". Differentiate term by term to 0 for every n.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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a. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x in an open interval (-c, c), then a, = b, for every n. (Hint: Let f(x) = E0a,x" = show that a, and b, both equal f®(0)/(n!).) b. Show that if Eo a,x" = 0 for all x in an open interval (-c, c) then a,n E=ob,x". Differentiate term by term to 0 for every n.
Transcribed Image Text:a. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x in an open interval (-c, c), then a, = b, for every n. (Hint: Let f(x) = E0a,x" = show that a, and b, both equal f®(0)/(n!).) b. Show that if Eo a,x" = 0 for all x in an open interval (-c, c) then a,n E=ob,x". Differentiate term by term to 0 for every n.
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