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SOVA2 [1]
3 years ago
6

How do I factorise 42 - 66x

Mathematics
1 answer:
lisov135 [29]3 years ago
6 0
The answer is 6(-11x+7)
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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
1.5 g = __?__ kg<br><br> 3 1-4 qt =__?__ pt<br><br> Help Is Appreciated!!!
zysi [14]
The first one is 0.0015
6 0
3 years ago
Tom bought 2.1 pounds of each type of fruit shown on the sign. What was the total cost of the fruit he brought.
Artist 52 [7]

Answer:

Can I see the sign?

Step-by-step explanation:

5 0
3 years ago
Which of the following is an example of a perfect square trinomial?
Aliun [14]

Answer:

c

Step-by-step explanation:

A perfect square trinomial is always in the form

(a+b)(a+b)= a^{2} +2ab+b^2

ie. (x+4)(x+4)= x^{2} +8x+16

4 0
3 years ago
Please help is this answer are right, number 1 and question #2
VladimirAG [237]
Yes. They are both right.
7 0
3 years ago
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