Exercise 6.6.10. Consider f(x) = en (x+1) f(x)=en(x+1) (a) Generate the Taylor series for f centered at zero, and use Lagrange's Remainder Theorem to show the series converges to f on (0,1). (The case x < is more straightforward while x requires some extra = care.) What happens when we attempt this with x > (b) Use Cauchy's Remainder Theorem proved in Exercise 6.6.9 to show the series representation for f holds on [0, 1).
Exercise 6.6.10. Consider f(x) = en (x+1) f(x)=en(x+1) (a) Generate the Taylor series for f centered at zero, and use Lagrange's Remainder Theorem to show the series converges to f on (0,1). (The case x < is more straightforward while x requires some extra = care.) What happens when we attempt this with x > (b) Use Cauchy's Remainder Theorem proved in Exercise 6.6.9 to show the series representation for f holds on [0, 1).
Chapter6: Exponential And Logarithmic Functions
Section6.2: Graphs Of Exponential Functions
Problem 52SE: Prove the conjecture made in the previous exercise.
Question
Please answer part a
Transcribed Image Text:Exercise 6.6.10. Consider f(x) = en (x+1)
f(x)=en(x+1)
(a) Generate the Taylor series for f centered at zero, and use Lagrange's
Remainder Theorem to show the series converges to f on (0,1). (The
case x < is more straightforward while x requires some extra
=
care.) What happens when we attempt this with x >
(b) Use Cauchy's Remainder Theorem proved in Exercise 6.6.9 to show the
series representation for f holds on [0, 1).
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