Consider the functions C: RC(x)=Σn=0R and S: R → R defined by2n(-1)" x ²m(2n)!and S(x)=Σn=0C(x + y) = C(x)C(y) — S(x)S(y) for all x, y & R.Show in particular thatC(x)² + S(x)² = 1 for all x & RFix an arbitrary a & R and consider the function g: R → R defined byg(x) = C(x)C(a − x) - S(x)S(a − x).-show that g is constant and conclude thatn 2n+1(-1)"x²(2n+1)!

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Consider the functions C: R → R and S: R → R defined by C(x) = Σ n=0 (-1)" x ² (2n)! and S (x) = 00 Σ n=0 (-1)"x²m+1 (2n+1)! Fix an arbitrary a & R and consider the function g: R → R defined by g(x) = C(x)C(a − x) – S(x)S(a − x). show that g is constant and conclude that C(x + y) = C(x)C(y) - S(x)S(y) for all x, y & R. Show in particular that C(x)² +S(x)² = 1 for all x & R

Consider the functions C: R → R and S: R → R defined by C(x) = Σ n=0 (-1)" x ² (2n)! and S (x) = 00 Σ n=0 (-1)"x²m+1 (2n+1)! Fix an arbitrary a & R and consider the function g: R → R defined by g(x) = C(x)C(a − x) – S(x)S(a − x). show that g is constant and conclude that C(x + y) = C(x)C(y) - S(x)S(y) for all x, y & R. Show in particular that C(x)² +S(x)² = 1 for all x & R

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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