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Use power series operations to find the Taylor series at x 0 for the following function.6x2-1212 cos xThe Taylor series for cos x is a commonly known series. What is the Taylor series at x = 0 for cos x?Σ(Type an exact answer.)n 0Use power series operations and the Taylor series at x 0 for cos x to find the Taylor series at x 0 for the given functionΣ(Type an exact answer.)n 2

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Use power series operations to find the Taylor series at x 0 for the following function.
6x2-1212 cos x
The Taylor series for cos x is a commonly known series. What is the Taylor series at x = 0 for cos x?
Σ
(Type an exact answer.)
n 0
Use power series operations and the Taylor series at x 0 for cos x to find the Taylor series at x 0 for the given function
Σ
(Type an exact answer.)
n 2
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Use power series operations to find the Taylor series at x 0 for the following function. 6x2-1212 cos x The Taylor series for cos x is a commonly known series. What is the Taylor series at x = 0 for cos x? Σ (Type an exact answer.) n 0 Use power series operations and the Taylor series at x 0 for cos x to find the Taylor series at x 0 for the given function Σ (Type an exact answer.) n 2

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Step 1

The Taylor series for...

f(x) cos x,f(0) =1
f'(x)sin f'(0) = 0
_
f"(x)cos:f(0)=-1
Taylor series for cosx at x = 0 is,
(x) xa)"
n!
n-0
- a)+ (a)(x-a +.
(a)+(a)
...
1!
2!
=/(0)+(x-0)+0x-0*+..
1!
2!
1+0(x-0)-1(x-0)
+...
2!
=1-
+.
2!
(-1)" x
(2n)
77
2n
n-0
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f(x) cos x,f(0) =1 f'(x)sin f'(0) = 0 _ f"(x)cos:f(0)=-1 Taylor series for cosx at x = 0 is, (x) xa)" n! n-0 - a)+ (a)(x-a +. (a)+(a) ... 1! 2! =/(0)+(x-0)+0x-0*+.. 1! 2! 1+0(x-0)-1(x-0) +... 2! =1- +. 2! (-1)" x (2n) 77 2n n-0

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