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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