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Consider the functions C: R → R and S: R → R defined by 00 Σ Σ n=0 n=0 Define a constant to be 2x where x is the first positive zero of C(x) Show that C(x) = n 2n == (-1)"x² (2n)! and S(x) C() = 0, s() = 1 C(TT) 1, S(T) = 0 C(2T) = 1, S(2T) = 0 = (-1)" x ²" + (2n+1)!

Consider the functions C: R → R and S: R → R defined by 00 Σ Σ n=0 n=0 Define a constant to be 2x where x is the first positive zero of C(x) Show that C(x) = n 2n == (-1)"x² (2n)! and S(x) C() = 0, s() = 1 C(TT) 1, S(T) = 0 C(2T) = 1, S(2T) = 0 = (-1)" x ²" + (2n+1)!

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1E
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Consider the functions C: R → Rand S: R → R defined by C(x) = n 2n (-1)"x² (2n)! == and S(x) Σ n=0 Define a constant to be 2x where x is the first positive zero of C(x) Show that C() = 0,S() = 1 C(TT) 1, S(T) = 0 C(2T) = 1, S(2T) = 0 00 Σ n=0 = 2n+1 (-1)" x ²"+ (2n+1)!
Transcribed Image Text:Consider the functions C: R → Rand S: R → R defined by C(x) = n 2n (-1)"x² (2n)! == and S(x) Σ n=0 Define a constant to be 2x where x is the first positive zero of C(x) Show that C() = 0,S() = 1 C(TT) 1, S(T) = 0 C(2T) = 1, S(2T) = 0 00 Σ n=0 = 2n+1 (-1)" x ²"+ (2n+1)!
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