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madreJ [45]
3 years ago
12

Are 5/6 and -4.713 on the same side or the opposite side of zero ?

Mathematics
1 answer:
Alchen [17]3 years ago
8 0
They are on opposite sides of zero because one number is negative and one is positive
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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that
Bond [772]

Taylor series is f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2}  }

To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have

f(x) = ln(x)

f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }

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.

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Since we need to have it centered at 9, we must take the value of f(9), and so on.

f(9) = ln(9)

f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }

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.

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Following the pattern, we can see that for f^{n}(x),

f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} }  \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}

This applies for n ≥ 1, Expressing f(x) in summation, we have

\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}

Combining ln2 with the rest of series, we have

f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2}  }

Taylor series is f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2}  }

Find out more information about taylor series here

brainly.com/question/13057266

#SPJ4

3 0
2 years ago
F(x) = 2x² + 8x Find f(-1)​
inysia [295]

Answer:

-6

Step-by-step explanation:

2(-1)^2 + 8*-1 = 2*1+8*-1=2-8=-6

8 0
3 years ago
Read 2 more answers
За^n(а^n + a^n-1) what is it??
solniwko [45]
Distribute the 3a^n to all the other values then solve...
(3a^n*a^n)+(3a^n*a^n)+(3a^n*-1)
4a^2n+4a^2n-3a^n=
8a^2n-3a^n
8 0
4 years ago
Jayla bought a table and some chairs at a furniture store.
anzhelika [568]

Answer:

b. She paid $30 for each chair.

6 0
3 years ago
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The value 0.01 gram is equivalent to 1 hectogram True or False
klemol [59]

Answer:

This is false statement.

Step-by-step explanation:

⇒ 1 Gram = 0.01 hectogram

⇒ 1 hectogram = 100 gram

⇒ 0.01 gram = 0.0001 hectogram

Thus the given statement is false.

3 0
3 years ago
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