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Yuliya22 [10]
2 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]2 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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Add 34+(−212) using the number line. Select the location on the number line to plot the sum.
Korvikt [17]

Answer:

Answer is explained below in the explanation section.

Step-by-step explanation:

Solution:

For this question, we need to have a number line, we can not make the number line here. As it will be very long. Instead, I have attached a number line from -11 to +11 for your understanding and explained it below. Please refer to the attachment below for the number line.

Number Line:

A number line is a line which contains all the numbers from negative infinity to positive infinity divided by a single number zero. It has two sides, left hand side and right hand side. A side left to zero contains all the negative numbers and a side right to 0 contains, all the positive numbers.

So,

We are asked to add 34 in (-212), we will get 178 but with the negative sign, and it will lie on the left hand side of the number line.

SO,

34 + (-212) = 34 - 212 = -178

Hence,

Our sum which is 178 will lie on the left hand side of the number line.

4 0
3 years ago
What is the whole number 13 as an improper fraction
DanielleElmas [232]
13/1 I hope that helped
5 0
3 years ago
RSM HOMEWORK HELP!!! PLEASE HELP ME ASAP!!
frutty [35]

Answer:

x = 27

Step-by-step explanation:

AC // DE

m∠ABD ≅ m∠BDE = 72°

m∠ADB + m∠BDE + m∠EDF = 180°

2x + 72° + 2x = 180°

4x = 108°

x = 27°

4 0
3 years ago
Is -8 = 8
madam [21]
No solution

The answer is D
5 0
2 years ago
PLEASE HELP ME!!! QUICKLY!!
podryga [215]

Answer:

4

Step-by-step explanation:

2L=w

32=LxW

so you put the 2L as the w

which is 32=Lx2L

32=2L^2

16=L^2

4=L

*To find the width you input 4 as L*

So 8=W

The shortest side would be 4

3 0
1 year ago
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