Question
Asked Nov 20, 2019
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Find the first 6 non-zero terms of the Taylor series expanded at the given value of x=a below and write the function that results from those terms. Then use that to estimate the given value.

b. f(x)= x, a=1, v2
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b. f(x)= x, a=1, v2

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Expert Answer

Step 1

Given function is

f(x) x
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f(x) x

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Step 2

Taylor series expansion formula of f(x) around point x = a is

(x-a
(x-a)
f(x)= f(a)+f(aXx-a)+f"(a)(x-a
2!
+f
3!
f
4!
(x-a)
f*IT"(a)
5!
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(x-a (x-a) f(x)= f(a)+f(aXx-a)+f"(a)(x-a 2! +f 3! f 4! (x-a) f*IT"(a) 5!

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Step 3

Now, find the deriva...

f(x)= x x2
1
f(x)=
2
-1/2
1
f "(x)
4
-3/2
1 3
-5/2
f "(x)
4 2
13 5
42 2
1 3 5 7
9/2
4 2 2 2
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f(x)= x x2 1 f(x)= 2 -1/2 1 f "(x) 4 -3/2 1 3 -5/2 f "(x) 4 2 13 5 42 2 1 3 5 7 9/2 4 2 2 2

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Tagged in

Math

Calculus