f(x) = 1 1+x² Compute f(x) f'(x) f"(x) f""(x) f(iv)(x) = ƒ(v)(x) = = || = = = We see that for the odd terms ƒ(2k+¹)(0) = = f(x) = Σ k=0 f(0) ƒ'(0) ƒ" (0) f"" (0) f(iv) (0) = f(v) (0) x²k = || = = and we also see that for the even derivatives ƒ(²k) (0) = Hence the Taylor series for f centered at 0 is given by || ✔ ✔ ✓
f(x) = 1 1+x² Compute f(x) f'(x) f"(x) f""(x) f(iv)(x) = ƒ(v)(x) = = || = = = We see that for the odd terms ƒ(2k+¹)(0) = = f(x) = Σ k=0 f(0) ƒ'(0) ƒ" (0) f"" (0) f(iv) (0) = f(v) (0) x²k = || = = and we also see that for the even derivatives ƒ(²k) (0) = Hence the Taylor series for f centered at 0 is given by || ✔ ✔ ✓
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.
Chapter4: Calculating The Derivative
Section4.1: Techniques For Finding Derivatives
Problem 35E
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Question
Transcribed Image Text:f(x) =
=
1
1+x²
Compute
f(x)
f'(x)
f"(x)
f""(x)
f(iv)(x) =
f(u)(x) =
||
=
||
=
=
||
∞
f(x) = Σ
k=0
←
f(0)
ƒ'(0)
f"(0)
f"" (0)
x2k
f(iv) (0)
=
=
||
=
=
=
We see that for the odd terms f(2k+¹) (0) =
and we also see that for the even derivatives f(2k) (0) =
Hence the Taylor series for f centered at 0 is given by
ƒ(v) (0) =
||
FI
►
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