Consider the functions C: R → R and S: R → R defined by C(x) = = Σ n=0 n 2n (-1)"x² (2n)! and S(x) = Σ n=0 n 2n+1 (-1)"x² (2n+1)! Show that there is a least positive number x_ such that C(x) = 0 Assume C(x) > 0 for all x > 0. Show that S is increasing, C is decreasing and concave down and derive a contradiction.
Consider the functions C: R → R and S: R → R defined by C(x) = = Σ n=0 n 2n (-1)"x² (2n)! and S(x) = Σ n=0 n 2n+1 (-1)"x² (2n+1)! Show that there is a least positive number x_ such that C(x) = 0 Assume C(x) > 0 for all x > 0. Show that S is increasing, C is decreasing and concave down and derive a contradiction.
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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