4.2 Weekend Earnings (Will get brainlyest ¡ please respond)

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

RUDIKE [14]

The taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 $(x+4)^{2}$ /2!+...........

Given a function f(x)=9/x,a=-4.

We are required to find the taylor series for the function f(x)=8/x centered at the given value of a and a=-4.

The taylor series of a function f(x)= $f(a)+f^{1}(a)(x-a)/1!+ f^{11}(a)(x-a)^{2} /2! +f^{111}(a)(x-a)a^{3}/3!+..........$

Where the terms in f prime $f^{1}$ (a) represent the derivatives of x valued at a.

For the given function.f(x)=8/x and a=-4.

So,f(a)=f(-4)=8/(-4)=-2.

$f^{1}$ (a)= $f^{1}$ (-4)=-8/( $-4)^{2}$

=-8/16

=-1/2

The series of f(x) is as under:

f(x)=f(-4)+ $f^{1}(-4)(x+4)/1!+ f^{11}(-4)(x+4)^{2}/2!.............$

$=8/(-4)-8/(-4)^{2} (-4)(x+4)/1!+ 24/(-4)^{3} (-4)(x+4)^{2}/2!.............$

=-2+2(x+4)/1!-24/16 $(x+4)^{2}$ /2!+...........

Hence the taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 $(x+4)^{2}$ /2!+...........

Learn more about taylor series at brainly.com/question/23334489

#SPJ4

3 0

1 year ago

PLEASE HELP (50 Points)....

Vedmedyk [2.9K]

Total deposit = 645.30 + 645.30 = $1290.60

Total withdrawals= 158.25 +168.36+157.42+148.46 = $632.49

Balance = 398.26 + 1290.60 - 632.49 = $1056.37

4 0

3 years ago

Read 2 more answers

2x^3+5x^2+6x+152x 3 +5x 2 +6x+15

Dmitrij [34]

ANSWER = 154^3+10^2+12+15

5 0

3 years ago

Solve: 3x-5y= -15 using y=mx+b method. Show steps

Sliva [168]

3x-5y=-15 What you do to one side, you must do to the other.
-3x -3x
-5y=-3x-15

-5y=-3x - 15
-5 -5 -5

Final Answer: y=3/5x + 3

4 0

3 years ago

Read 2 more answers

Type the correct answer in each box. If necessary, use /for the fraction bars

Vikentia [17]

Answer:

The experimental probability of rolling an odd number is 60%, which is 10% more than the theoretical probability.

Step-by-step explanation:

The complete question is:

Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).

A special 8-sided die is marked with the numbers 1 to 8. It is rolled 20 times with these outcomes.

3, 4, 5, 2, 7, 1, 3, 7, 2, 6, 2, 1, 7, 3, 6, 1, 8, 3, 5, 6

The experimental probability of rolling an odd number is _%, which is _% more than the theoretical probability.

Solution:

The possible outcomes of rolling an 8-sided die are:

S = {1, 2, 3, 4, 5, 6, 7, 8}

The odd numbers are:

Odd = {1, 3, 5, 7} = 4 outcomes

The theoretical probability of rolling an odd number is:

$P_{T}(\text{Odd})=\farc{4}{8}=\frac{1}{2}=50\%$

Now from the given 20 outcomes the odd values are:

Odd = {3, 5, 7, 1, 3, 7, 1, 7, 3, 1, 3, 5} = 12 outcomes

Compute the experimental probability of rolling an odd number as follows:

$P_{E}(\text{Odd})=\frac{12}{20}=\frac{3}{5}=60\%$

Thus, the experimental probability of rolling an odd number is 60%, which is 10% more than the theoretical probability.

6 0

3 years ago