Answered: 53) Which function f(x) = E anx"… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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Question

Solve both 52 and 53 please

f(n) (0)
52) To show that a function f (x) is equal to its Taylor Series
x" at some
n!
n=0
xo E R,
fen (0) " converges at xo-
a) it suffices to show that
п!
n=0
00
b) it suffices to show that f"(0),
n!
converges absolutely at xo.
n=0
c) it suffices to show that lim Rn.o(xo)
0.
n-00
flr) (0)
d) f(x) is always equal to >
x" for all x E R.
п!
n=0
e) None of the above.

53) Which function f(x) = E anx" satisfies the differential equation
n=0
f'(x) = -2x f (x)?
a) f(x) = E(-1)"
n!
n=0
b) f(x) = E(-1)"
(2n)!
n=0
c) f(x) = E(-1)n-12n=1
n!
n=0
.2n+1
d) f(x) = Ë(-1)"-1=*1
n!
n=0
e) None of the above.

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