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5. In future courses, you'll meet sequences of functions. For instance, consider we could define a sequence (fn) of functions fn: R→ R inductively via fo(x) = 1, fn+1(x) :=1+ for fn (1) dt Compute the functions f₁, f2 and f3. The sequence (fn) should seem familiar if you think back to elementary calculus; why?

5. In future courses, you'll meet sequences of functions. For instance, consider we could define a sequence (fn) of functions fn: R→ R inductively via fo(x) = 1, fn+1(x) :=1+ for fn (1) dt Compute the functions f₁, f2 and f3. The sequence (fn) should seem familiar if you think back to elementary calculus; why?

Advanced Engineering Mathematics
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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5. In future courses, you’ll meet sequences of *functions*. For instance, consider we could define a sequence \((f_n)\) of functions \(f_n : \mathbb{R} \to \mathbb{R}\) inductively via \[ f_0(x) \equiv 1, \quad f_{n+1}(x) := 1 + \int_0^x f_n(t) \, dt \] Compute the functions \(f_1, f_2\) and \(f_3\). The sequence \((f_n)\) should seem familiar if you think back to elementary calculus; why?
Transcribed Image Text:5. In future courses, you’ll meet sequences of *functions*. For instance, consider we could define a sequence \((f_n)\) of functions \(f_n : \mathbb{R} \to \mathbb{R}\) inductively via \[ f_0(x) \equiv 1, \quad f_{n+1}(x) := 1 + \int_0^x f_n(t) \, dt \] Compute the functions \(f_1, f_2\) and \(f_3\). The sequence \((f_n)\) should seem familiar if you think back to elementary calculus; why?
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