f(x) =11+x²Computef(x)f'(x)f"(x)f""(x)f(iv) (x) =f(v) (x)======We see that for the odd terms f(2k+¹) (0)∞f(x) = Σk=0f(0)ƒ'(0)f" (0)f"" (0)f(iv) (0) =f(v) (0)x2k||=||===and we also see that for the even derivatives f(2k) (0)Hence the Taylor series for f centered at 0 is given by=►✔►←

The given function is f(x) =11+x2 To find all the derivatives we here use the quotient rule of…

f(x) = 1+x² Compute f(x) f'(x) f"(x) f""(x) f(iv) (x) = f(¹)(x) = = = = = ✔ f(x) = Σ k=0 f(0) ƒ'(0) f"(0) f"" (0) f(iv) (0) = f(v) (0) x²k = = || = = We see that for the odd terms ƒ(2k+1) (0) = 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+x² Compute f(x) f'(x) f"(x) f""(x) f(iv) (x) = f(¹)(x) = = = = = ✔ f(x) = Σ k=0 f(0) ƒ'(0) f"(0) f"" (0) f(iv) (0) = f(v) (0) x²k = = || = = We see that for the odd terms ƒ(2k+1) (0) = and we also see that for the even derivatives ƒ(²k) (0) = Hence the Taylor series for f centered at 0 is given by = ✔

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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