The Maclaurin series for f(x) is f(x) = 16x^2 - 914.6667x^3 + O(x^4).
To find the Maclaurin series for the function f(x) = 8x^2sin(7x), we need to compute its derivatives and evaluate them at x=0:
f(x) = 8x^2sin(7x)
f'(x) = 16xsin(7x) + 56x^2cos(7x)
f''(x) = 16(2cos(7x) - 49xsin(7x)) + 112xcos(7x)
f'''(x) = 16(-98sin(7x) - 343xcos(7x)) + 112(-sin(7x) + 7xcos(7x))
f''''(x) = 16(-2401cos(7x) + 2401xsin(7x)) + 784xsin(7x)
At x=0, all the terms with sin(7x) vanish, and we are left with:
f(0) = 0
f'(0) = 0
f''(0) = 32
f'''(0) = -5488
f''''(0) = 0
Thus, the Maclaurin series for f(x) is:
f(x) = 32x^2 - 2744x^3 + O(x^4)
We can also find the coefficients directly by using the formula:
cn = f^(n)(0) / n!
where f^(n)(0) is the nth derivative of f(x) evaluated at x=0. Using this formula, we get:
c0 = f(0) / 0! = 0
c1 = f'(0) / 1! = 0
c2 = f''(0) / 2! = 32 / 2 = 16
c3 = f'''(0) / 3! = -5488 / 6 = -914.6667
c4 = f''''(0) / 4! = 0 / 24 = 0
Therefore, the Maclaurin series for f(x) is:
f(x) = 16x^2 - 914.6667x^3 + O(x^4)
Learn more about Maclaurin series here
https://brainly.com/question/28170689
#SPJ11
-1/2x-8=hx-8 what does h equal?
Answer:
H = -1/2
Step-by-step explanation:
Find the perimeter of the semicircle below. Use 3.14 for
pi.
1.6 ft
Answer:
8.2ft
Step-by-step explanation:
Perimeter of a whole circle = 2*pi*r with radius r
Here we have 1.6ft as the radius so the whole circle's perimeter would be
2 * 3.14 * 1.6 = 10.048
We have half the circle so we half this number to 5.024.
Now we have to add the bottom straight line, which is two radii (two lots of 1.6)
5.024 + 1.6 + 1.6 = 8.224 which is rounded to 8.2ft
What is perimeter and area of this object?
Answer:
Step-by-step explanation:
You have a circle with radius r = 3 ft and a 3-by-12 rectangle.
Area of circle = πr² = 9π ft²
Area of rectangle = 3 × 12 = 36 ft²
Total area = 36 + 9π ≈ 64.3 ft²
Perimeter of circle = 2πr = 6π ft
Perimeter of rectangular projections = 18 ft
Total perimeter = 6π +18 ≈ 36.8 ft
A house is located at the center of a circular lot, exactly 10 yards from the edge of the lot. How much fencing will the homeowner need to surround the entire lot?
What is 0=0
Infinite solution or no solution?
Answer:
no solution i think hehe 0=0
96 / 2^5 - 2 please help asap
Answer:
1 is the right answer
Hope it helps!
Thanks!
Answer:
It equals 1.
Step-by-step explanation:
2^5=32, 96/32=3, 3-2=1.
3x-2y= 10
Write the slope intercept for of the equation
Answer: y = -3/2x + 5
Step-by-step explanation:
Answer:
y= 3/2x - 5
Step-by-step explanation:
Slope intercept form is y=mx + b
1. subtract 3x from both sides -2y= -3x + 10
2. divide -2 on each value y= 3/2x - 5
3. simplify if needed (already in simplest form)
6 1/4 - 2 3/4 = ?
please help lol
Answer:
3 1/2
Step-by-step explanation:
Rewriting our equation with parts separated
=6+1/4−2−3/4=6+1/4−2−3/4
Solving the whole number parts
6−2=4/6−2=4
Solving the fraction parts
1/4−3/4=−2/4 1/4−3/4=−2/4
Reducing the fraction part, 2/4,
−2/4=−1/2−2/4=−1/2
Combining the whole and fraction parts
4−1/2=3 1/2
How many kilograms of chocolate will each person get if 4 people share 13 of a kilogram of chocolate equally?
Step-by-step explanation:
hope it helps
plz rate my answer
Which set of ordered pairs does not represent a function?
O {(0,6), (5,-4), (3, -4), (8,-6)}
O {(6,-1), (-6, -1),(-2,-8),(-4,9)}
O {(-3, -3), (4,1),(-3,3), (2, 2)}
O {(1,-4), (5, -7), (-3,-6), (-2,-4)}
cuantas monedas de 20 son 15€ ?
Answer: 75
Step-by-step explanation:
If (2,-6) is rotated 90 degrees clockwise what would be the coordinates
Answer:
Step-by-step explanation:
Rotating (2,-6) 90 degrees results in (6,2)
According to the Marshall’s survey, 80 sixth graders, or 40% of the students in sixth grade like to have school remote. How many sixth graders are there in Marshall Middle School?
NEED HELPPPP
Answer:
200
Step-by-step explanation:
If 80 represents 40% of the total then 10% = 20
100% of the total: 20 x 10 = 200
simplify (2/9 × 45/15) - 7/24
I hope this helps! have an amazing day!
Answer:
3/8
Step-by-step explanation:
(2/9 x 45/15) - 7/24
45/15 = 3
(2/9 x 3) - 7/24
2/9 x 3 = 6/9 = 2/3
2/3 - 7/24
2/3 = 16/24
16/24 - 7/24 = 9/24
9/24 = 3/8
Rashaad went to the store to buy some apples. The price per pound of the apples is $4.75 per pound and he has a coupon for $2.50 off the final amount. With the coupon, how much would Rashaad have to pay to buy 5 pounds of apples? Also, write an expression for the cost to buy
p
p pounds of apples, assuming at least one pound is purchased.
Answer:
21.75
Step-by-step explanation:
sorry if im wrong
Which equation is not linear?
y = –3x + 4
y = 6x
y = 3
y = x5 – 1
Answer:
y=3 maybe
Step-by-step explanation:
The area of the figure is how many square units?
Answer:
hope it helped
have a nice day mate
The time T takes to buy a fuel at a petrol station varies directly as the number of vehicles V on a quare and inversely as the number of pumps P available in the station. In a station with pumps, it took 10minutes to uel 20 vehicles. Find 1. The relationsip between T, P and V. 2. The time it will take to fuel 50 vehicles in the station with 2 pumps. 3. The number of pumps required to fuel 40 vehicles in 20 minutes.
Answer:
The time T takes to buy a fuel at a petrol station varies directly as the number of vehicles V on a quare and inversely as the number of pumps P available in the station. In a station with pumps, it took 10minutes to uel 20 vehicles. Find 1. The relationsip between T, P and V. 2. The time it will take to fuel 50 vehicles in the station with 2 pumps. 3. The number of pumps required to fuel 40 vehicles in 20 minutes.
-0.1=-10c. Solve each equation
Answer:
c = 0.01
Step-by-step explanation:
divide both sides by -10 to isolate c
-0.1 = -10c
/-10. /-10
0.01 = c
c = 0.01
que es la regla de los signos
Answer:
La regla de los signos son los positivos y los negativos.Pero otra cosa son cuales son las raglas de los signos.
Simplify negative 4 and 1 over 4 − negative 9 and 1 over 2. Help ;---;
Answer:
-53/4
Step-by-step explanation:
=-4+1/4-9+1/2
=-16+1-36+2/4
=-53/4
WHO HAS READ THE PEARL, BY JOHN STEINBECK( IN NEED OF HELP FAST) EMMERGENCY
Answer:
me me me omg
Step-by-step explanation:
HELLP!! U WILL GET I,000 POINTS Alistair writes the system of equations below. 2x+3y=−60 2x+3y=120 ------------------------------------------------------------------------------------------------------------------------ Which statement describes the solution to this system of equations? There is exactly (2,3) There is exactly one solution (-60,120) There is no solution to the systems of equations There are infinite numbers of the solution to the system
Answer:
Step-by-step explanation:
Does it say what x and y equals
Answer: there is no solution to the system of equation
Step-by-step explanation:
C
A circle has an area of 113 square centimeters. What is the radius of the circle?
So, first you want to have 113 then you are going to want to divide it by pi or 3.14. After that, square it.
Your answer would be 6
What is the surface area of a sphere with radius 4?
A. 16 units2
B. 12x units 3
C. 3290 units2
D. 644 units2
Answer:
a
Step-by-step explanation:
you need to divide the entire amount of
Can someone reply with how this works
At 6:00 A.M., the temperature was 10º below zero. During the day, the temperature rose an average of 2º per hour. If h represents the number of hours since 6:00 A.M., which equation represents the temperature T?
Answer:
10+2h=T
hope this helps :)
Which fraction is equivalent to 1/6?
Answer:
There could be many answers: 2/12, 3/18, 4/24...
Step-by-step explanation:
You never really gave options but all you do is just take 1/6 and multiply the top and bottom by a certain number to get what you're looking for, for example 1/6 times 2, both on the top and bottom will get you 2/12 because 1 times 2 is 2 and, 6 time 2 is 12. :)
Answer:
2/12 6/36 there's alot more
Hey if someone could please help me with this i waould be very greatful
Answer:
40%
Step-by-step explanation:
2/5x100%=40%
A medium pizza at Pizzaz Pizza
costs $12 plus 1.00 per topping,
A medium pizza at Crustie's
Pizza costs $10 plus $1.50 per
topping. How many toppings
does it take so that a medium
pizza costs the same at each
pizzeria? Define your variables,
write a system of equations, and
solve
Answer:
21
Step-by-step explanation:
Answer:
it would take four toppings so that a medium pizza would cost the same at a pizzeria