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Yuliya22 [10]
3 years ago
6

Enter the coefficients of the fifth Taylor polynomial T5(x) for the function f(x) = x5−3x4+2x2+5x−2 based at b=1. T5(x)= + (x−1)

+ (x−1)2+ (x−1)3+ (x−1)4+ (x−1)5. NOTE: This exercise gives a method for writing a polynomial in powers of x−1 instead of powers of x. This may be useful, for example, if you are interested in the values of the polynomial near x=1 .
Mathematics
1 answer:
DENIUS [597]3 years ago
5 0

Compute the necessary values/derivatives of f(x) at x=1:

f(1)=3

f'(1)=2

f''(1)=-12

f'''(1)=-12

f^{(4)}(1)=48

f^{(5)}(1)=120

Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) f(x) at x=1 by

T_5(x)=\dfrac3{0!}+\dfrac2{1!}(x-1)-\dfrac{12}{2!}(x-1)^2-\dfrac{12}{3!}(x-1)^3+\dfrac{48}{4!}(x-1)^4+\dfrac{120}{5!}(x-1)^5

T_5(x)=3+2(x-1)-6(x-1)^2-2(x-1)^3+2(x-1)^4+(x-1)^5

###

Another way of doing this would be to solve for the coefficients a,b,c,d,e,g in

f(x)=a+b(x-1)+c(x-1)^2+d(x-1)^3+e(x-1)^4+g(x-1)^5

by expanding the right hand side and matching up terms with the same power of x.

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A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There a
Verdich [7]

Using the permutation formula, it is found that there are 17,297,280 different signals consisting of 8 flags.

In this problem, the order in which the flags are visited is important, hence the <em>permutation formula</em> is used to solve this question.

<h3>What is the permutation formula?</h3>

The number of possible permutations of x elements from a set of n elements is given by:

P_{(n,x)} = \frac{n!}{(n-x)!}

The first flag is blue, then the remaining 7 are taken from a set of 14, hence:

P_{(14,7)} = \frac{14!}{7!} = 17,297,280

There are 17,297,280 different signals consisting of 8 flags.

More can be learned about the permutation formula at brainly.com/question/25925367

8 0
2 years ago
What is the probability that a value falls in the interval μ ± 2σ, that computes the probability P(-2 &lt; Z &lt; 2). Round to f
bija089 [108]

Answer:

0.9544    

Step-by-step explanation:

P(-2 < Z < 2) means that Z has mean 0 and standard deviation 2.

P(−2 < Z < 2) = F(2) - F(-2)

Using the Z - table,

F(2) = 0.9772

and F(-2) = 0.0228

Thus,

P(−2 < Z < 2) = 0.9772 - 0.0228 = 0.9544

This means that data within two standard deviation is 95%.

8 0
3 years ago
Help me with all of them plzzz eleven<br><br> Points
irina [24]
122 with 58
35 with 145
62 with 118
105 with 75
5 0
3 years ago
Read 2 more answers
Can someone please help me!!!
egoroff_w [7]
The correct answer is the first one(a): To get the system B,..., the first equation multiplied by 4...

Explanation:

1. Let us first multiple the first equation in System A with 4, we would get:
4(2x - y) = 4 * 3

=> 8x - 4y = 12 --- (A)

Now add the equation (A) and the second equation of System A:

8x  - 4y = 12
3x + 4y = 10
------------------
11x = 22 

Hence,
System B:
2x - y = 3
11x = 22

-i
5 0
3 years ago
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What is the value of this expression when a=20
Aloiza [94]

Answer:

20

Step-by-step explanation:

A=20

4 0
2 years ago
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