Answers
Compute the first few derivatives to reveal a pattern:
f(x) = x sin(x)
f '(x) = x cos(x) + sin(x)
f ''(x) = (-x sin(x) + cos(x)) + cos(x) = -x sin(x) + 2 cos(x)
f '''(x) = (-x cos(x) - sin(x)) - 2 sin(x) = -x cos(x) - 3 sin(x)
f ''''(x) = (x sin(x) - cos(x)) - 3 cos(x)) = x sin(x) - 4 cos(x)
f ⁽⁵⁾(x) = (x cos(x) + sin(x)) + 4 sin(x) = x cos(x) + 5 sin(x)
f ⁽⁶⁾(x) = (-x sin(x) + cos(x)) + 5 cos(x) = -x sin(x) + 6 cos(x)
f ⁽⁷⁾(x) = (-x cos(x) - sin(x)) - 6 sin(x) = -x cos(x) - 7 sin(x)
f ⁽⁸⁾(x) = (x sin(x) - cos(x)) - 7 cos(x) = x sin(x) - 8 cos(x)
and so on.
The pattern should be clear: for some integer k,
• if n = 4k, then f ⁽ⁿ ⁾(x) = x sin(x) - n cos(x)
• if n = 4k + 1, then f ⁽ⁿ ⁾(x) = x cos(x) + n sin(x)
• if n = 4k + 2, then f ⁽ⁿ ⁾(x) = -x sin(x) + n cos(x)
• if n = 4k + 3, then f ⁽ⁿ ⁾(x) = -x cos(x) - n cos(x)
80 is a multiple of 4, so the 80th derivative falls in the first category. Then
f ⁽⁸⁰⁾(x) = x sin(x) - 80 cos(x)
Related Questions
The graph of y = 4x2 - 4x – 1 is show
Use the graph to find estimates for
the solutions of
i) 4x2 - 4x – 1 = 0
Answers
Answer:
Here we have the equation:
y = 4*x^2 - 4*x - 1
And we should have the graph (you can see it below this answer)
Now we want to find the solutions of:
4*x^2 - 4*x - 1 = 0
These solutions will be the two values of x at which the graph of our function intersects the line y = 0, that is the x-axis.
Then we need to find the two values of x at which our graph intersects the x-axis.
In the graph, we can estimate the solutions as:
x = -0.2
x = 1.2
To find the exact solutions we can use the Bhaskara's equation, and we will find that the solutions are given by:
[tex]x = \frac{-(-4) +- \sqrt{(-4)^2 - 4*4*(-1)} }{2*4} = \frac{4+ -\sqrt{32} }{8} = \frac{4 +-5.66}{8}[/tex]
Then the two solutions are:
x = (4 + 5.66)/8 = 11.2075
x = (4 - 5.66)/8 = -0.2075
Please help I need it
Answers
C is the hypotenuse, the side opposite from the 90 degree angle. So we have C and A.
c^2 - a^2 = b^2
23^2 - 16^2 = b^2
b^2 = 273
b= 16.5
What are the two consecutive whole numbers that the quotient for 86 ÷ 11 is between?
Answers
Answer:
Umm i need the answer to that question to lol haha...
Step-by-step explanation:
lmk if you got the answers
Answers
Step-by-step explanation:
area of trapezium= 1/2×sum of parallel sides× height
=1/2×(9+9+7)×8
=1/2×25×8
=100
I hope this helps( ╹▽╹ )♥
a cone with a radius of 3 cm and a height of 3 cm
Answers
Answer: ⇒V=π×32×53=45×π3≈47.124 cubic cm
Hope this helps!!
How Many Times Done 16 go Into 78!??!!!!?!!?!??!?!?! HELP ME!!!
Answers
Answer:
4.87500
Step-by-step explanation:
hope this helps
Answer:
4.875
Step-by-step explanation:
78 divided by 16 = 4.875
Find the absolute value of each of the following numbers.
2.54
17.65
14.2
90.44
Answers
|7.65|= 7.65, take out the lines
|-14.2|= 14.2, take out lines and inside signs
|90.44|= 90.44, take out the lines
Hope this helps!! :D
how do I know that 15/30 is greater than 1/3 but less than2/3
Answers
Answer:
ok simple. lets start with 15/30, 15/30 is basically 1/2 because 15 is half of 30
1/3 is not to the half point of 3 the half point of 3 is 1/5. 2/3 is more than halfway of 3 as it is more than 1.5/3. Do I make sense?
Step-by-step explanation:
hope this helps!!
is 24 root 4 or 16 bigger
Answers
Answer:
no
Step-by-step explanation:
Answer:
16 is bigger.
Step-by-step explanation:
This about it like this: The bigger the root numeral the higher.
Find the length between (1, 3) and (5, 6)
Answers
Answer:
5
Step-by-step explanation:
Find the slope of the line that passes through the given point (-2, -4) and (-11, -7)
Answers
Answer:
Step-by-step explanation:
[tex]Slope= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-7-[-4]}{-11-[-2]}\\\\=\frac{-7+4}{-11+2}\\\\=\frac{-3}{-9}\\\\=\frac{1}{3}[/tex]
Help. I’m confused on this question and would like an answer. Thanks.
Answers
Answer:
Angle
Step-by-step explanation:
Since, the figure is in the final step of construction. So, it will have only two rays which as we can see are emerging from a common point.
So, it represents an angle.
An angle has two rays arising out of a common vertex point.
HELP ME FAST PLSSS<3
A bottle of juice states that a serving is 1/2 cup. How many servings are in a 2-pint container? (one pint= 2 cups)
Answers
Answer: 8 servings
Step-by-step explanation:
1/2 cup + 1/2 cup = 1 cup
> 1 cup + 1 cup = 2 cups = one pint
1/2 cup + 1/2 cup = 1 cup
if 4 servings go in one pint then 8 servings goes in 2 pint
Answer:
8 cups/servings.
Explanation:
Can't explain further more because I'm not good in explaining things yet I'm sure that's the correct answer.
If want to spend EXACTLY all $40. This means no
money is left. How many pairs of socks ($4) and
gloves ($5) do I have to buy?
Answers
Answer:
You would buy 4 pairs of socks and 4 pairs of gloves.
Step-by-step explanation:
5x4= 20
4x5=20
20+20=40
There are 10 students. 30% of the students returned their calculators at the end of class. How
many students returned their calculator at the end of class?
Answers
We can find 10% by dividing the number of students by 10.
10/10 = 1
We need to work out 30%, and we already have 10% so we just multiply 10% by 3.
1 x 3 = 3
So 30% = 3
Therefore, 3 students retuned their calculator at the end of class.
For the image above, which action below allows the scale to be balanced?
Add 3 blocks to the right side.
Add 4 blocks to the right side.
Take away 3 blocks from the left side.
Take away 5 blocks from the left side.
Answers
Answer:
B is correct
Step-by-step explanation:
I took the flvs test
The action to make both side balanced
Take away 5 blocks from the left side.
What is Balanced?In science, if an object is still, we say it is balanced. An object is in an equilibrium state when it is balanced. Any forces acting on the object are counterbalanced by forces moving the other way. The average location of the gravitational pull on an object is known as the centre of gravity.
We have the figure.
On right side there are total 8 weights.
and, on left there are total 3 weights.
So, the difference of blocks on
= 8- 3
= 5 blocks
So, take away 5 blocks from left.
Learn more about Balanced here:
https://brainly.com/question/1443731
#SPJ3
(-3-√80)/6
please simplify
Answers
(-3 - 4√5)/6
Amelia started with $54, and spent $6 each day at camp. She has $18 left. Write and solve an equation to find how many days d Amelia was at camp
Answers
equation: 54-18=36 36 divided by 6 = 6
06.07 equivalent expressions module six project 1 part2
Answers
Answer:
go to utube.com/RyStone and sub he has the answers
Step-by-step explanation:
Hes op
Add the polynomials: (3x+3x2-4x+5) + (x3-2x2+x-4)
Answers
Answer......
x^2+3x+1
Answer:
The answer is x^2+3x+1
Step-by-step explanation:
The perimeter of the first rectangle below is 120 inches. The perimeter of the second rectangle is 180 inches. What are the values of x and v?
A. x = 6; v = 42
B. x = 13; v = 42
C. x = 42; v = 6
D. x = 48; v = 28
Answers
Answer:
A
Step-by-step explanation:
Answer:
A. x = 6; v = 42
Step-by-step explanation:
Strategy : Guess and Check
Let's start with A:
If x = 6, then the first rectangle would be 12 + 42 + 6 + 12 + 42 + 6 = 120
Let's see if this checks out with the second rectangle.
6 + 42 + 42 + 6 + 42 + 42 = 180
algebra question 14
help me please
Answers
Answer:
I don't know but I got 3x sorry I might be wrong
5 × 3/2, but the answer as a fraction
Answers
Answer:
15/2
Step-by-step explanation:
5/1 * 3/2 = 15/2
- The side length of a square is 4x3 cm. What is the area of the square?
Answers
Answer:
144 cm
Step-by-step explanation:
If there is no sign between a number and a letter in an expression, what does that imply?
A: division
B: multiplication
C: subtraction
D: addition
Answers
What is 2/4 as a decimal and percent
Answers
Answer:
0.5 is 2/4 as a decimal and 50% is 2/4 as a percent
Complete the inequality for this graph.
y
Answers
5
Step-by-step explanation:I had the same exact question and 6 was incorrect but when I tried 5 it passed. Hope this helped and have a good one!
The linear inequality that represents the graph will be y < x + 5.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
From the graph, the two points are (0, 5) and (-5, 0). Then the linear inequality is given as,
(y - 0) < [(5 - 0) / (0 + 5)](x + 5)
y < x + 5
The linear inequality that represents the graph will be y < x + 5.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
Question number 8 is in the picture below.
Answers
Answer:
7 / 10 < 11 / 12
Step-by-step explanation:
cross multiply
Find the surface area of the pyramid. The side lengths of the base are equal.
Thank you in advance
Answers
Answer:
195.6
Step-by-step explanation:
area of base= 1/2 * 8 * 6.9 = 27.6
area of lateral face= 1/2 * 8 * 14 = 56
total surface area = 27.6 + 56 + 56 + 56 = 195.6
pleased help me! I need the question it due today.
Answers
Answer:
7. -21-15g
8. x+3y+7
Step-by-step explanation:
use multiplication for number 7
number 8 is just rearranging the numbers
number 9 is confusing since i don't know if it's a point or another symbol