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 Rn(x) → 0.] f(x) = 2x − 4x3, a = −1 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 10(x + 1) + 12(x + 1)2 − 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 10(x + 1) + 4(x + 1)2 − 12(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 + 10(x + 1) + 12(x + 1)2 + 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 12(x + 1) + 10(x + 1)2 − 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 + 10(x + 1) + 4(x + 1)2 + 12(x + 1)3
Answers
Answer:
f(x) = 2 - 10 (1 + x) + 12 (1 + x)^2 - 4 (1 + x)^3
Step-by-step explanation:
The general form of the series is shown in the attachment. For the purpose here, we need to evaluate f(-1), f'(-1), f''(-1) and so on.
f(x) = 2x -4x^3; f(-1) = 2(-1)(1 -2(-1)^2) = (-2)(-1) = 2
f'(x) = 2 -12x^2; f'(-1) = 2 -12(-1)^2 = -10
f''(x) = -24x; f''(-1) = -24(-1) = 24
f'''(x) = -24; f'''(-1) = -24
So, the series is ...
f(x) = 2 -10(x +1)/1! +24(x +1)^2/2! -24(x +1)^3/3!
f(x) = 2 -10(x +1) +12(x +1)^2 -4(x +1)^3 . . . . . . . matches the first choice
Related Questions
What statement accurately describes the scatter point?
A. There are three distinct clusters.
B. There are no outliers.
C. There is one outlier.
D. There are two outliers.
Answers
PI is the _ of a circle's _ to its _
Answers
Answer:
ratiocircumferencediameterStep-by-step explanation:
Pi is the ratio of a circle's circumference to its diameter.
_____
We suspect you have answer choices for filling in these blanks. Besides the words shown above, there are other ways they can be filled:
Pi is the ratio of a circle's area to its radius squared.
Pi is the measure of a circle's central angle to its diameter endpoints.
What is the sum in simplest form I ready diagnostic please hurry
Answers
example:
The value of x is 22
Step-by-step explanation:
We are given that there are two numbers
First number is x
second number is 35
The sum of x and 35 is 57
so, we get equation as
now, we can solve solve x
So, subtract both sides by 35
A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches averaged 863 calories. The economist claims that after the testing period ends, the average caloric content of Virginia School lunches drops significantly.
Set up the null and alternative hypotheses to test the economist’s claim.
Answers
Answer:
Null hypothesis: u = 863
Alternate hypothesis (H1): u < 863
Step-by-step explanation:
a. Null hypothesis: u = 863
The null hypothesis implies that the average caloric content of Virginia School lunches is equal to 863.
b. Alternate hypothesis: u < 863
The alternate hypothesis implies that the average caloric content of Virginia School lunches is less than 863, that is, it drops significantly.
Solve for a given 2e^a =4b
Answers
Answer:
a = ln (2b)
Step-by-step explanation:
2e^a =4b
Divide each side by 2
2/2 e^a =4/2b
e^a = 2b
Take the natural log of each side
ln(e^a) = ln(2b)
a = ln (2b)
Question 11 of 15
Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45
millimeters. How much water can Micah fill in his cup?
Answers
Answer:
36.644 mL . . . . depending on your value of π (see below)
Step-by-step explanation:
The height of Micah's cup is found from the radius and slant height. The radius is half the diameter, so is 36 mm. Then the height h is ...
45² = 36² +h²
h = √(45² -36²) = 27 . . . . . mm
The volume is given by the formula ...
V = (1/3)πr²h
V = (1/3)π(36 mm)²(27 mm) = 11664π mm³
For π = 3.14
11664(3.14) mm³ ≈ 36,625 mm³ = 36.625 mL
For π = 3.14159265
11665π mm³ = 36,644 mm³ = 36.644 mL
_____
Comment on units
A unit of measure used for relatively small volumes, especially of liquid, is milliliters (mL). 1 mL = 1000 mm³.
Answer:
The answer is 11664pimm^3
Step-by-step explanation:
list all the factor means use divisibility rules of 102,232
Answers
Answer:
102,232 = 2·2·2·13·983
Step-by-step explanation:
102,232 ends in 32, so is divisible by 4
102,232/4 = 25558 ends in 2, so is divisible by 2
25558/2 = 12779
is not even, so is not divisible by 2
has a sum of digits mod 9 of 8, so is not divisible by 3 or 9
does not end in 0 or 5, so is not divisible by 5
gives the result 1277-2·9 = 1259; 125-2·9 = 107; 10-2·7 = -4, which is not zero, so 12779 is not divisible by 7
gives the result (1+7+9)-(2+7) = 8, which is not divisible by 11, so 12779 is not divisible by 11
gives the result 1277 +4·9 = 1313, which is divisible by 13, so 12779 is divisible by 13
12779/13 = 983 needs to be tested for divisibility by primes between 17 and 31, namely 17, 19, 23, 29, 31. It is not divisible by any of these, so this is the last prime factor of 102,232:
102,323 = 2·2·2·13·983
_____
Divisibility rules:
Note that for any transformation rule, the rule can be repeated on the reduced result. The digits of a sum of digits can be summed, for example.
2: ends in even digit
3: sum of digits is divisible by 3
5: ends in 0 or 5
7: subtracting 2 times the last digit from the rest is divisible by 7
11: difference of sums of alternate digits is divisible by 11
13: there are several rules. A couple of useful ones are
the sum of 4 times the last digit and the remaining number will be divisible by 13 (used above)the difference of the sums of alternate groups of 3 digits will be divisible by 13 (232-102 = 130, for the number above; is divisible)17: subtracting 5 times the last digit from the rest is divisible by 17
19: the sum of 4 times the last 2 digits and the remaining number will be divisible by 19
23: the sum of 3 times the last 2 digits and the remaining number will be divisible by 23
29: the sum of 9 times the last 2 digits and the remaining number will be divisible by 29
31: subtracting 3 times the last digit from the rest is divisible by 31
−5y=−5
7x+6y=7
Is (5,1) a solution of the system
Answers
Answer:no, (5,1) is not a solution for the equation. (1/7,1) will be a solution for the equation.
Step-by-step explanation:
one way to do it is to plug 1 as the y-value into the first equation which does work but when you plug 5 as the x-value and 1 as the y-value in the second equation, it will get you to 41 which does not match so it will not be an equation. the other way to check is to solve by substitution which for the first equation, you divide both side by -5 and get y=1 then substitute y with 1 in the second equation and subtract both side by 6 and get 7x=1 and divide both side by 7 to get 1/7. the y-value match but the x-value don't so (5,1) is not a solution.
Three black beads, two red beads, and a yellow bead are arranged in a line. What is the probability that no black bead is adjacent to the yellow bead?
Answers
Answer:
Probability of no black bead is adjacent to the yellow bead is = 0.966
Step-by-step explanation:
First to arrange all the beads without restrictions = 6! = 720
Probability the black bead is adjacent to Yellow bead = 4!/6! = 24 /720
= 0.0333
Probability of no black bead is adjacent to the yellow bead is
= 1- Probability the black bead is adjacent to Yellow bead
= 1-0.033
= 0.966
tickets for a concert have been in increadbibly high demand. and as the date for the concert draws closer the price of tickets increases exponentially. the cost of a pair of concert tickets was $96 yesterday and today it is $108.
what is the multiplier
what is the daily percent rate?
using the cost of a ticket today as your initial value write an exponential equation that models this situation
what will be the cost of a pair of concert tickets in one week from today
what was the cost of a pair of tickets three days ago?
Answers
Answer:
multiplier 1.125percent rate 12.5%p(t) = 108·1.125^tp(7) = $246.32p(-3) = $75.85Step-by-step explanation:
a) The daily multiplier is 108/96 = 1.125
b) The daily percentage change is 1.125 -1 = .125 = 12.5%
c) The function can be written as ...
price = (initial value)·(daily multiplier)^t
p = 108·1.125^t
d) for t=7, put the number in and do the arithmetic.
108·1.125^7 ≈ 246.32 . . . dollar cost in a week
e) same deal, for t=-3
108·1.125^-3 ≈ 75.85 . . . .dollar cost 3 days ago
Need help. not in college
Answers
Factor.
Z^2- 3z – 18
Answers
Answer:
(z-6)(z+3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
z^2-6z + 3z -18
z(z-6)+3(z-6)
(z+3)(z-6)
What are prime number
Answers
A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.
In other words, prime numbers are the numbers
divisible by 1 and the number itself.
For example, let us take 2.
2 has only two factors and those are 1 and 2 so it's prime.
Similarly, 7 is also a prime number because it has only two factors
and these are 1 and the number itself which is 7.
Answer:
A number that is only divisible by itself and 1
Step-by-step explanation:
How many unique ways are there to arrange the letters in the word PRIOR?
Answers
Answer:
60
Step-by-step explanation:
Answer:
it is 60
Step-by-step explanation:
How many fish a are in the box
Answers
Answer:
Where is the box?
Step-by-step explanation:
So I can help you
Find the supplement of an angle that measures 20 degrees.
A) 50 degrees
B) 70 degrees
C) 90 degrees
D) 160 degrees
Answers
Answer:
160 degrees
Step-by-step explanation:
Answer:I think it is D
Step-by-step explanation:
faz um bom tempo que não faço expressões numéricas,vcs podem me ajudar!
Answers
Answer:
English Plz
Step-by-step explanation:
B(4,8) and C(8,0) are the endpoints of a line segment. What is the midpoint M of that line
segment?
Write the coordinates as decimals or integers.
Answers
Answer:
(6,4)
Step-by-step explanation:
I just did quick math in my head.
Complete A and B for 5-8 points.
Answers
Answer:
a) 4 hours
b) 11 am
Step-by-step explanation:
So say the number of hours is x
a) 72 + 6x = 96
6x = 24
x = 4
b) 7am + 4 hours = 11am
The angle of elevation from the top of a building to the top of another is 45°.
The distance between the feet of these two buildings is 402 m.
What is the distance between the top of the two buildings?
Answers
Answer:
402m
Step-by-step explanation:
Set this up as a triangle and use trig to solve it:
tan(45) = y/402
y = 402*tan(45)
substitute: tan(45) = 1
y = 402 * 1
y = 402m
What’s the correct answer for this?
Answers
Answer:
C
Step-by-step explanation:
HJN IS SIMILAR TO PQN
What is the circumference of the following circle?
9 cm
Answers
Answer:
9π or 28.27 cm
Step-by-step explanation:
The circumference formula is 2πr or dπ. The diameter is 9 cm so we multiply 9 with pi to get the answer.
The value of the circumference of the given circle is 9π cm OR 28.278 cm
Calculating circumference of a circleFrom the question, we are to determine the circumference of the circle.
The circumference of a circle can be calculated by using the formula,
C = πd
Where C is the circumference of the circle
and d is the diameter
From the diagram,
d = 9 cm
Therefore,
Circumference of the circle = π × 9
Take π = 3.142
Then,
Circumference of the circle = 28.278 cm
Hence, the value of the circumference of the given circle is 9π cm OR 28.278 cm
Learn more on Calculating circumference of a circle here: https://brainly.com/question/12823137
What is the length of AC? Brainliest for right answer
Answers
Answer:
2.3 units
Step-by-step explanation:
In the diagram, the measure of angle 9 is 85°
Which angle must also measure 85°?
<2
<5
<11
<12
Please help, need answer ASAP !! :)
Answers
Answer: 11
Step-by-step explanation:
Vertically opposite angles
Answer: <11
Step-by-step explanation:
<9 and <11 are vertical angles, so they are congruent.
This area model shows 50 X 38 Which number is missing from the model
Answers
Answer:
69
Step-by-step explanation:
Select the correct symbol to compare the rates.
22 miles in 20 minutes 38 miles in 30 minutes
Answers
Answer:
<
Step-by-step explanation:
22/20=1.1
38/30=1.27
Answer:
<
Step-by-step explanation:
An experiment involves rolling a die and drawing a card from a standard deck of 52 cards.
What is the probability that the die lands on 4 and the card is a heart?
Enter your answer as a reduced fraction, like this: 3/14
Answers
Answer:
1/24
Step-by-step explanation:
1 of the 6 possible rolls is a 4, meaning there is a 1/6 probability of rolling 4.
13 of the 52 cards are hearts, meaning that there is a 1/4 probability of drawing a heart.
1/6 * 1/4 = 1/24
What is volume of a cylinder with base area 64pi cm² and a height equal to twice the radius? Give your answer in terms of pi.
512 pi
256 pi
1024 pi
4096 pi
Answers
Answer:
1024 pi
Step-by-step explanation:
The area formula is ...
A = πr^2
So, the radius is ...
r = √(A/π)
For the given area, the radius of the cylinder is ...
r = √(64π/π) = 8 . . . . cm
The height is said to be twice this value, so is 16 cm.
__
The volume of the cylinder is found from ...
V = Bh
where B is the base area and h is the height. Our cylinder has a volume of ...
V = (64π cm^2)(16 cm) = 1024π cm^3
what are the steps for using integar tiles to evaluate the expression 45 divided by 15
Answers
Answer:
1. Gather 45 tiles
2. Split them up into groups of 15. Your answer will be the amount of piles you end up with. Hope this helps!
brainliest quick!
Aiden wanted to model -15 + 15 = 0 on the number line. He first drew an arrow 15 units long starting from zero that pointed to the left. He then draws another arrow 15 units long starting from zero that points to the right. What error did Aiden make?
A. The first arrow he drew should have pointed to the right to represent -15.
B. The second arrow he drew should have pointed to the left to represent 15.
C. The first arrow he drew should have started at -15 instead of 0.
D. The second arrow he drew should have started at -15 instead of 0.
Answers
Answer:
c
Step-by-step explanation:
Answer:
it's D
Step-by-step explanation:
The number never goes over 0 so there is no need to put anything above 0
