ctions C: R → Rand S: R → R defined by (x) = Σ n=0 2n (-1)" x ²m (2η)! and S(x) ) = 5(x)C(v) + C(x)S() for x, y ε = Σ n=0 (-1) x (2n+

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.
Chapter6: Applications Of The Derivative
Section6.4: Related Rates
Problem 3E: Assume x and y are functions of t. Evaluate dydtfor each of the following. 2xy5x+3y3=51;...
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Consider the functions C: R → R and S: R → R defined by
Show that
C(x)
=
Σ
n=0
2n
(-1)"x²
(2n)!
and S(x)
S(x + y)= S(x)C(y) + C(x)S(y) for x, y & R
=
Σ
n=0
n 2n+1
(-1)"x
(2n+1)!
Transcribed Image Text:Consider the functions C: R → R and S: R → R defined by Show that C(x) = Σ n=0 2n (-1)"x² (2n)! and S(x) S(x + y)= S(x)C(y) + C(x)S(y) for x, y & R = Σ n=0 n 2n+1 (-1)"x (2n+1)!
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