Answers
Answer:
(x − π)⁷ / 5040
(x − 1)³ / 16
Step-by-step explanation:
Taylor series expansion of a function is:
f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(x₀) / n! (x − x₀)ⁿ
where f⁽ⁿ⁾(x₀) is the nth derivative evaluated at x₀.
For the first problem, f(x) = sin x and x₀ = π. We want the seventh degree term, so n = 7.
The seventh degree term is therefore: f⁽⁷⁾(π) / 7! (x − π)⁷
Find the seventh derivative of sin x:
f(x) = sin x
f⁽¹⁾(x) = cos x
f⁽²⁾(x) = -sin x
f⁽³⁾(x) = -cos x
f⁽⁴⁾(x) = sin x
f⁽⁵⁾(x) = cos x
f⁽⁶⁾(x) = -sin x
f⁽⁷⁾(x) = -cos x
Evaluated at π, f⁽⁷⁾(x) = 1. So the seventh degree term is (x − π)⁷ / 5040.
For the second problem, f(x) = √x and x₀ = 1. We want the third degree term, so n = 3.
The third degree term is therefore: f⁽³⁾(1) / 3! (x − 1)³
Find the third derivative of √x:
f(x) = √x
f⁽¹⁾(x) = ½ x^-½
f⁽²⁾(x) = -¼ x^-³/₂
f⁽³⁾(x) = ⅜ x^-⁵/₂
Evaluated at 1, f⁽³⁾(x) = ⅜. So the third degree term is (x − 1)³ / 16.
Related Questions
John spent $75 on a shopping trip for new clothes last week. He had expected to spend $100 on clothes. Complete the table.
A 6-column table with 1 row. Column 1 is labeled Approximate Value with entry 100 dollars. Column 2 is labeled Exact Value with entry 75 dollars. Column 3 is labeled Error with entry 25 dollars. Column 4 is labeled Absolute Error with entry 25 dollars. Column 5 is labeled Ratio with entry e. Column 6 is labeled Percent Error with entry f.
What is the ratio? e =
What is the percent error? f =
Answers
Answer:
I think it would be Column 2
Step-by-step explanation:
Answer:
What is the ratio? e = 25/75
What is the percent error? f = 33%
Step-by-step explanation:
What is 6 2/3 x 1 1/2
Answers
Answer:
6 2/3 x 1 1/2 is 10
Step-by-step explanation:
Use the graph of y = sin x to find all values of x, 0 < x < 2pi, for which the following is true. (Enter your answers as a comma-separated list.)
sin x = 0
Answers
Answer:
if x = pi/2, then y =1.
if x = pi/4, then y = [tex]\frac{\sqrt{2 } }{2}[/tex]
if x = pi, then y = 0
Step-by-step explanation:
The required answer as a comma-separated lists are (0, 0), ([tex]\frac{\pi}{6}[/tex], 0.5), ( [tex]\frac{\pi}{4}[/tex], [tex]\frac{1}{\sqrt{2} }[/tex]), ( [tex]\pi[/tex], 0)
Given the equation of a sine graph expressed as:
[tex]y=sinx[/tex] for all values of x within the range 0 < x < 2π
We need to get the value of y for the values of x within the range as shown:
If x = 0;
y = sin0
y = 0
The required solution is (0, 0)
If x = 30;
y = sin30
y = 0.5
The required solution is ([tex]\frac{\pi}{6}[/tex], 0.5)
If x = [tex]\frac{\pi}{4}[/tex];
y = sin [tex]\frac{\pi}{4}[/tex]
y = [tex]\frac{1}{\sqrt{2} }[/tex]
The required solution is ( [tex]\frac{\pi}{4}[/tex], [tex]\frac{1}{\sqrt{2} }[/tex])
If x = [tex]\pi[/tex]
y = sin [tex]\pi[/tex]
y = 0
The required solution is at ( [tex]\pi[/tex], 0)
If x = [tex]2\pi[/tex]
y = sin[tex]2\pi[/tex]
y = 0
Hence the required answer as a comma-separated lists are (0, 0), ([tex]\frac{\pi}{6}[/tex], 0.5), ( [tex]\frac{\pi}{4}[/tex], [tex]\frac{1}{\sqrt{2} }[/tex]), ( [tex]\pi[/tex], 0)
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Consider the function f(x)=xln(x). Let Tn be the nth degree Taylor approximation of f(2) about x=1. Find: T1, T2, T3. find |R3| <= ?
Answers
Answer:
R3 <= 0.083
Step-by-step explanation:
f(x)=xlnx,
The derivatives are as follows:
f'(x)=1+lnx,
f"(x)=1/x,
f"'(x)=-1/x²
f^(4)(x)=2/x³
Simialrly;
f(1) = 0,
f'(1) = 1,
f"(1) = 1,
f"'(1) = -1,
f^(4)(1) = 2
As such;
T1 = f(1) + f'(1)(x-1)
T1 = 0+1(x-1)
T1 = x - 1
T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2
T2 = 0+1(x-1)+1(x-1)^2
T2 = x-1+(x²-2x+1)/2
T2 = x²/2 - 1/2
T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3
T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3
T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)
Thus, T1(2) = 2 - 1
T1(2) = 1
T2 (2) = 2²/2 - 1/2
T2 (2) = 3/2
T2 (2) = 1.5
T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)
T3(2) = 4/3
T3(2) = 1.333
Since;
f(2) = 2 × ln(2)
f(2) = 2×0.693147 =
f(2) = 1.386294
Since;
f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).
Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,
Since;
f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2
Finally;
R3 <= |2/(4!)(2-1)^4|
R3 <= | 2 / 24× 1 |
R3 <= 1/12
R3 <= 0.083
A car is sold for $18,000. After one year, the value of the car is $9,900. Write an exponential function y to determine the value of
the car after x years if the rate of decrease is the same each year.
y =
Estimate the value of the car after 6 years. Round the answer to the nearest dollar.
Answers
Answer:
temperature and kinctic energy are related
Abhasra bought nine fancy pens for a total of $44.01. How much did each pen cost?
A.) $4.21
B.) $4.89
C.) $4.42
D.) $396.09
Answers
Answer:
B.) $4.89
Step-by-step explanation:
44.01 ÷ 9 = 4.89
Answer:
B) $4.89
Step-by-step explanation:
44.01/9 = 4.89
44.01 = the total amount
9 = the amount of pens he got
to check your work you can do 4.89 x 9 which equals 44.01
1. Find the selling price. Cost of a sled: $99.50. Markup: 95%
2. Find the selling price. Original price of a book: $18.50. Discount: 45%
Answers
Answer:
Number 2 is 10 dollars and 17 cents
Number 1 is 194 dollars and 2 cent
Step-by-step explanation:
Determine whether the given ordered pair is a solution of the system.
(1, -8)
y = 5x - 13
2x + 4y = - 30
Answers
Fred can paint a 30-foot fence in 5 hours. Which of the following is true?
Answers
Answer:
lol
Step-by-step explanation:
Which is larger 10.5 or 10.50
Answers
Answer:
10.5 is really 10.50 the . 5 is half the whole one unit, like 50 cents is half a dollar
three-fourths of a number is at least -18
Answers
Answer:
3/4*X < -18
( put a line underneath the less than sign ) ( Astric's means multiplication )
Step-by-step explanation:
Hope this helped, Have a Wonderful Day!!
Answer:
x ≥ - 24
Step-by-step explanation:
Let's solve this with an equal sign and then decide how to handle the at least part.
3/4 x = -18 Multiply by 4
3/4 * 4 x = -18*4 Cancel the left, multiply the right.
3x = -72 Divide by 3
x ≥ -24
You need the greater than to indicate that 3/4 of a number can give something larger than - 18.
You need the equal sign to fulfill at least.
At least, in this question means "get larger."
so x > - 24
solve (x-4)^2=5.
Answers:
A. x=9 and x=1
B. x=5+(square root)4
C. x=-4+(square root)5
D. x=4+(square root)5
Answers
Answer:
don't dout yourself
Step-by-step explanation:
never give up thanks for the free points
does it look like I play any sports?? if so what sports
Answers
Answer:
ayyyye i play soccer too lol
Step-by-step explanation:
Answer:
looks like you play softball or basketball
Step-by-step explanation:
Which ordered pairs are solutions to the equation 5x+12y=15?
Answers
• (0,5/4)
• (1,5/6)
• (2,5/12)
Hope this helps!
f(x)=-2x^2+14/x^2-49 which statement describes the behavior of the graph of the function shown at the vertical asymptotes?
Answers
Answer:
Option 3 :
x → 7+, y → –[infinity]
Step-by-step explanation:
f(x) = (-2x² + 14)/(x² - 49)
x² - 49 = (x + 7)(x - 7)
Hence f(x) goes to infinity at x = - 7 or 7
x < - 7 = (-ve)(-ve) = + ve
=> x → –7–
Here, x² - 49 is + ve
-7 < x < 7 = (+ve)(-ve) = - ve
=> x → –7+ or x → 7– .
here, x² - 49 is - ve
x > 7 = (+ve)(+ve) = + ve
=> x → 7+
Here, x² - 49 is + ve
So (-2x² + 14) is - ve for all [ x → –7– , x → –7+ , x → 7– , x → 7+ ]
As,
-2(-7)² + 14 = -84 and -2(+7)² + 14 = -84
x → –7– = (-ve)/(+ve)
=> y → -[infinity].
x → –7+ or x → 7– = (-ve)/(-ve)
=> y → [infinity]
x → 7+ = (-ve)/(+ve)
=> y → -[infinity].
x → 7+, y → –[infinity]. is the correct option
The statement (C) as x approaches 7 from the left, y approaches -∞ describe the behavior of the graph of the function.
What is a function?It is defined as a spceial type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a rational function:
[tex]\rm f(x) =\dfrac{-2x^2+14}{x^2-49}[/tex]
x² - 49 cannot be zero:
x² - 49 ≠ 0
x ≠ 7, x ≠ -7
From the graph, as x approaches 7 from the left, y approaches -∞
Thus, the statement (C) as x approaches 7 from the left, y approaches -∞ describe the behavior of the graph of the function.
Learn more about the function here:
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In science class, Polly learned that trees help make the oxygen that people breathe. One tree makes about 250 pounds of oxygen each year. Polly wonders how much oxygen the trees on her street make. When she gets home, she counts 32 trees on her street. How many tons of oxygen do they make in a year?
Answers
Answer:
They make 4 approximately tons of oxygen each year.
Step-by-step explanation:
( 250lbs × 32 ) ÷ 2000 = 4t
250 pounds because each tree makes about 250 pounds of oxygen a year.
× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.
÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.
If 7x + 5y = 25 and 3x + 2y = 10, what is the value of x +y?
Answers
Answer:
Step-by-step explanation:
7x+5y=25
3x+2y=10
21x+15y=75
21x+6y=30
0x+11y=45
11y=45
y=45/11
y = 4.09
sub in 4.09 into equation 1
7x+5(4.09)=25
7x+20.45=25
7x=25-20.45
x=4.55/7
PLEASE HELP ILL GIVE AS MANY POINTS AS YOU WANT!!!
And to some reason this was deleted???! Cause I didn’t mean to if I did
Answers
Answer:
1. Take the value of X and replace X with that value in the equation.
2. Now you solve Y.
How many grams are in 1 Bag of suger
Answers
Answer:
One pound of granulated sugar converted to gram equals to 453.59 g. How many grams of granulated sugar are in 1 pound? The answer is: The change of 1 lb ( pound ) unit in a granulated sugar measure equals = into 453.59 g ( gram ) as per the equivalent measure and for the same granulated sugar type.
Among various populations of plants or animals, diseases spread exponentially. Use the function y = 8000(1 - e^-0.03t) to model the spread of Common Corn Rust through a field of 8000 corn plants, with t equal to the number of days since the first case of the disease. How many plants will be infected with Common Corn Rust after 10 days?
Answers
Answer:
It's 2073 on edge2020
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
on edge 2020
64 divided by 12 4/5
Answers
Answer:
..............5
Step-by-step explanation:
64 ÷12 4/5
Question 1 of 10
What is the slope of the line shown below?
10
(3,9)
O A.
5
B. 4
(1,1)
-5
10
15
O C. -
1
4
O D.-4
SUBMIT
Answers
The slope of the given line is 4.
What is slope?The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Given that, a line passing through points (3, 9) and (1, 1) we need to find the slope of the line,
Slope = y₂ - y₁ / x₂ - x₁
So,
Slope = 9-1 / 3-1 = 8/2 = 4
Hence, the slope of the given line is 4.
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A case of bottled juice contains 30 bottles.Each case contained a total of 507 ounces of juice.Which equation represents the relationship between ounced of juice,y and number of bottles,x A.y=16.9x+30B.y=0.6x C.y=30x+16.9D.y=16.9x
Answers
Step-by-step explanation:
the answer is D (y=16.9)
I divided 507 and 30 and got the answer 16.9.
if you would've put any other answer it would've been wrong because the answer had the 30 in it after it was divided.(not sure if its 100% correct)
I need help pleaseeeee
Answers
Please mark me as brainless if right
Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. He made $243 selling tickets. How many adult tickets did he sell?
Answers
Answer:
30
Step-by-step explanation:
12x4=48
243-48=195
195/6.50= 30
hope that helps :)
What’s an expotential function
Answers
Answer:
Overview of the exponential function
The exponential function is one of the most important functions in mathematics (though it would have to admit that the linear function ranks even higher in importance). To form an exponential function, we let the independent variable be the exponent. A simple example is the function
Please mark me brainliest if this helped you ! (by clicking the little crown on my answer) it helps a lot thnx! (≧∇≦)/
You deposit $2000 in an account earning 3% interest compounded monthly.How much will you have in the account in 15 years?
Answers
A = P * (1 + R/N)NT
Where A = the final amount
P = initial principal
R = interest rate
N = number of times interest is compounded per year
T = number of years
In this case
A = 2000 * (1 + .05/12) ^(12 * 18)
A = 2000 * (1.0041667) ^(180)
A = 2000 *(2.1137)
A = 4227.40
find percent increase
from 24 teachers to 30 teachers ___
Answers
It cost Randy $515.20 for new carpet in his bedroom. If the room is 11.5 feet wide by 14 feet long, what was the cost per square foot?
Answers
Answer:
$3.20
Step-by-step explanation:
First, find the area in square feet of his room:
Use the area formula, A = lw, where l is length and w is width:
A = lw
A = 14(11.5)
A = 161
So, his room is 161 square feet.
To find the cost per square foot, divide 515.20 by 161:
515.20/161
= 3.2
So, the cost per square foot was $3.20
What is the solution to the equation 23(y−6)=−(y+2)+1 2 3 ( y - 6 ) = - ( y + 2 ) + 1 ?
Answers
Answer:
Substitute the given value into the function and evaluate.
23 (y − 6) = −(y + 2) + 1 = y = 137/24
2 = y = 137/24
3 = y = 137/24
y − 6 = −(y + 2) + 1 = y = 5/2
