Answer:
[tex]\displaystyle f'(x) = 2x[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationDefinition of a Derivative: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = x^2[/tex]
Step 2: Differentiate
Substitute in function [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{(x + h)^2 - x^2}{h}[/tex]Expand: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{x^2 + 2hx + h^2 - x^2}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{2hx + h^2}{h}[/tex]Factor: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{h(2x + h)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} 2x + h[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Which expression is equivalent to 4/9 × 7
key:
1. 9÷4×7
2. 4×7÷9
3. 4÷7×9
4. 7×9÷4
Thank you :)
13
Use the circle below for
questions 13-16.
Answer:
NK=12
Step-by-step explanation:
x^2 +9^2=15^2
x^2+81=225
subtract 81
x^2=144
x=12
(This is only for number 13, I don't know the answer to 14-16)
Using the Pythagoras theorem, the value of NK is 12.
What is the Pythagoras theorem?The sum of the squares of the lengths of the other two sides of a right triangle equals the square of the hypotenuse's length.
It is given that, NL=9, and KL=15.
Use the Pythagoras theorem,
[tex]& \Rightarrow {{15}^{2}}=N{{K}^{2}}+{{9}^{2}} \\ & \Rightarrow 225-81=N{{K}^{2}} \\ & \Rightarrow NK=\sqrt{144} \\ & \Rightarrow NK=12 \\[/tex]
Therefore, the value of NK is 12.
Learn more about the Pythagoras theorem, here
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-> What is the remainder of 46 divided by 48?
the answer would be 0.9583
What is the area of a triangle with base 10 cm and height 17 cm
Answer:
85 cm
I have to use 20 characters to answer so extra space here :/
In order to determine her pulse rate, Michaela's nurse counted 24 beats in 15 seconds.
At this rate, how many beats would she have in 60 seconds?
in a class of 50 people 30 said that they spend 2 hours playing video games if was a true sample how many students out of a 800 in the school would say they also spend more than 2 hours playing video games
Answer:
480
Step-by-step explanation:
I received a $3 discount on a $20 phone case. What was the percent of discount?
find the hypotenuse if the base is 300 and altitude is 400
Answer:
okAy
Step-by-step explanation:
hypo(square) = altitude(square)+base,(square)
so hypo(square) =300(square)+400(square)
Answer:
500
Step-by-step explanation:
300² + 400² = 500²
pythagorean theorem
Plz help this is due today i would have done it myself but i totally forgot about these so PLZ HELP AND NO LINKS AND NO GROSS PICTURES OR I REPORT.
Answer:
Answer B will be the best answer for your question.
Step-by-step explanation:
Polygons usually have straight sides, but this one does not.
Consider the function g(x) = StartLayout Enlarged left-brace first row negative 9, x less-than 11 second row 7, x greater-than-or-equal-to 11 EndLayout.
What is Limit of g (x) as x approaches 11, if it exists?
–9
–1
7
DNE
The limit as g(x) approaches 11 doesn't exist.
[tex]\lim_{x \to 11} g(x) = DNE[/tex]
It looks like you are working with the following piecewise defined function:
[tex]g(x)=\left \{ {{-9;x<11} \atop {7;x\geq11}} \right.[/tex]
There is a rule in calculus that tells us that for a limit to exist, both lateral limits must be the same as x approaches a given value. This is:
[tex]\lim_{x \to a^{-}} f(x)=\lim_{x \to a^{+}} f(x)[/tex]
if and only if this is true, then:
[tex]\lim_{x \to a^{-}} f(x)=\lim_{x \to a^{+}} f(x)=\lim_{x \to a} f(x)[/tex]
if that condition isn't met, then the limit doesn't exist.
So let's calculate the lateral limits for this function:
[tex]\lim_{x \to 11^{-}} g(x) = -9[/tex]
This means that as x approaches 11 from the left, the function will return a value close to -9
Now, let's calculate the lateral limits for this function:
[tex]\lim_{x \to 11^{+}} g(x) = 7[/tex]
This means that as x approaches 11 from the right, the function will return a value close to 7
You can better visualize this in the graph of the function which I attached to this answer.
Notice that both lateral limits are different, from the left you got a -9 and from the right you got a 7. Therefore, according to the rule I wrote above, the limit does not exist.
For more information on this topic, you can go to the following link:
https://brainly.com/question/17334531?referrer=searchResults
Answer:
D) DNE
Step-by-step explanation:
edge 2021
State the relationship between the graphs of f(x) and g(x).
-5
5
X
X
a.
fand g are reflections of each other about the y-axis.
b. f and g are reflections of each other about the x-axis.
C. g is shifted to the left 5 units relative to f, otherwise they are the same.
d. g is shifted to the right 5 units relative to f, otherwise they are the same.
Answer:
B
Step-by-step explanation:
Calculated
As per the data, f and g are reflections of each other about the y-axis. The correct option is A.
What is graph?To graph is to create a diagram that depicts a relationship between two or more things. A graph can be made by drawing a series of bars on graph paper.
A graph (also known as an undirected graph to distinguish it from a directed graph or a simple graph to distinguish it from a multigraph) is a pair G = (V, E), where V is a set with vertices (singular: vertex) and E is a set of paired vertices with edges.
The relationship between the graphs of f(x) = -5/x and g(x) = 5/x is that they are reflections of each other about the y-axis.
To see this, note that replacing x with -x in f(x) gives f(-x) = -5/(-x) = 5/x, which is the same as g(x). Therefore, the graphs of f(x) and g(x) are symmetric with respect to the y-axis.
Thus, the correct option is A.
For more details regarding graph, visit:
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Your question seems incomplete, the probable complete question is:
State the relationship between the graphs of f(x) and g (x)
f(x) = -5/x, g )x) 5/x
a. f and g are reflections of each other about the y-axis.
b. f and g are reflections of each other about the x-axis.
c. g is shifted to the left 5 units relative to f, otherwise they are the same.
d. g is shifted to the right 5 units relative to f, otherwise they are the same.
Use the theorem in Sec. 28 to show that if f (z) is analytic and not constant throughout a domain D, then it cannot be constant throughout any neighborhood lying in D. Suggestion: Suppose that f(z) does have a constant value ωo throughout some neighborhood in D.
Answer:
The value of f(z) is not constant in any neighbourhood of D. The proof is as explained in the explaination.
Step-by-step explanation:
Given
For any given function f(z), it is analytic and not constant throughout a domain D
To Prove
The function f(z) is non-constant constant in the neighbourhood lying in D.
Proof
1-Assume that the value of f(z) is analytic and has a constant throughout some neighbourhood in D which is ω₀
2-Now consider another function F₁(z) where
F₁(z)=f(z)-ω₀
3-As f(z) is analytic throughout D and F₁(z) is a difference of an analytic function and a constant so it is also an analytic function.
4-Assume that the value of F₁(z) is 0 throughout the domain D thus F₁(z)≡0 in domain D.
5-Replacing value of F₁(z) in the above gives:
F₁(z)≡0 in domain D
f(z)-ω₀≡0 in domain D
f(z)≡0+ω₀ in domain D
f(z)≡ω₀ in domain D
So this indicates that the value of f(z) for all values in domain D is a constant ω₀.
This contradicts with the initial given statement, where the value of f(z) is not constant thus the assumption is wrong and the value of f(z) is not constant in any neighbourhood of D.
Solve for x:
3x - 6 = 12
Answer:
x = 6
Step-by-step explanation:
3x - 6 = 12
3x = 18
x = [tex]\frac{18}{3}[/tex]
x = 6
Which of the following graphs could be a representation of a geometric
sequence?
Answer:
Third one
Step-by-step explanation:
In geometric sequence, the graph must have one slope
The graphs could be a representation of a geometric
sequence are given by option (A), option (B) and option (D)
What is a geometric sequence?"It is a sequence in which the ratio between consecutive terms is equal."
For given question,
We need to identify the graphs that could be a representation of a geometric sequence.
A sequence [tex]a_1,a_2,...,a_n[/tex] is geometric sequence if [tex]\frac{a_2}{a_1}=r[/tex],
[tex]\frac{a_3}{a_2}=r[/tex],. . ., [tex]\frac{a_n}{a_{n-1}} = r[/tex]
This means, for geometric sequence the number being multiplied each time is constant.
And the geometric sequence is of the form
[tex]a_1,(a_1r),(a_1r^2),...[/tex]
If we graph the geometric sequence then it would be non-linear.
From above pattern of geometric sequence, we can say that the graph of the geometric sequence is exponential in nature.
Therefore, the graphs could be a representation of a geometric
sequence are given by option (A), option (B) and option (D)
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The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair.
Function 1 graph of function f of x equals negative x squared plus 8 multiplied by x minus 15 Function 2 f(x) = −x2 + 2x − 3
Function 1 has the larger maximum at (1, 4).
Function 1 has the larger maximum at (4, 1). Function 2 has the larger maximum at (1, −2).
Function 2 has the larger maximum at (−2, 1).
Answer:
A.) Function one has a larger maximum at (4,1)
Step-by-step explanation:
The function f(x) = -x² + 8x - 15 will have larger maximum at ( 4,1 ) so option (B) will be correct.
What is a function?
A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
A function can be regarded as a computer, which is helpful.
Given 1 function,
f(x) = -x² + 8x - 15
f(x) = -(x² - 8x + 15 )
f(x) = - [(x - 4)² - 16 + 15 ]
f(x) = -(x-4)² + 1
So vertex will at ( 4,1 )
In function 2,
f(x) = −x² + 2x − 3
f(x) = - [ x² - 2x + 3 ]
f(x) = -[ (x-1)² - 1 + 3 ]
f(x) = - (x-1)² - 2
So vertex will at ( 1, -2 )
Since in function(1) maximum is at y = 1 while in function (2) maximus is at y = -2
Hence Function 1 has the larger maximum at (4, 1).
For more about the function
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Will give the brainliest answer and 20 points to anyone who can give a complete answer and not a scam link or a joke answer or begging for points (those 3 types of answers will be reported)
A grocery store manager notices that this month her store sold a total of 571 gallons of ice cream, which represents a decrease of 18% from last month. How much ice cream did the store sell last month? Round your answer to the nearest integer.
The store sold ____________ gallons of ice cream last month.
Answer:
673.8
Step-by-step explanation:
The cost of three cans of pineapple at the grocery outlet is $2.25 on the cost of six cans of the same kind of pineapple is $4.80 at save market which store has a better price for pineapple grocery outlet or save market
Answer:
save market has a better price.
Step-by-step explanation:
2.25÷ 3= 0.75
4.80÷6= 0.8
A rectangular parking lot has a length that is yards greater than the width. The area of the parking lot is square yards. Find the length and the width.
Answer:
length = 18yd
Width = 10yd
Step-by-step explanation:
Complete question
A rectangular parking lot has a length that is 8 yards greater than the width. The area of the parking lot is 180 square yards. Find the length and the width.
Area of the parking lot - length * width
A = LW
Given
Area = 180sq. yd
If the parking lot has a length that is 8 yards greater than the width, then;
L = 8 + W
The area becomes;
A = (8+W)W
180 = 8W+W²
W²+8W - 180 = 0
W²+18W-10W - 180 = 0
W(W+18)-10(W+18) = 0
(W-10)(W+18) = 0
W-10 = 0
W = 10yd
Since L = 8 + W
L = 8 + 10
L = 18yd
Hence the length and the width area 18yd and 10yd respectively
plz help for a brainly
Answer:
364yd^2
Step-by-step explanation:
LxWxH
Answer:
its 364
Step-by-step explanation:
you do length times width times height
1 ) Ms. Allgood donated 63 books to her class. She would like to provide an equal number of books to each of her 9 students.
Answer:
7
Step-by-step explanation:
Answer: 7
Step-by-step explanation: 63 divided by 9 is 7, so Ms. Allgood can give all her 9 students 7 books each
k+5,-1 and 2k are consecutive terms of an arithmetic sequence.
1.find k
2.find the terms.
Answer:
K enejwjwjenenw
Step-by-step explanation:
Serey mejw catttsn keesuyboard
Follow the steps for dividing decimals. Then, round to two decimal places (hundredths).
1.476)6.380
Answer:
4.32
Step-by-step explanation:
The steps required are:
4.322
1.476 )6.380
5.904
____
0.476
0.4763
0.4428
_____
0.0335
0.03358
0.02952
_____
0.00406
0.004060
0.002952
_____
0.0011080
Therefore, the answer is 4.32.
SOLVE FOR X AND Y!!! DUE IN 2 HOURS!!!
Answer:
x = 5, y = 5
Step-by-step explanation:
The scale changes from 8 to x+y
to find the change in scale, use the bottom values.
2 + 3 = 5 | 1 + 3 = 4
5/4 = 1.25 (the scale)
8 * 1.25 = 10
x+y = 10
There are 2 possibilities for this, but I feel like it is possibility #1
1. x = 5, y = 5
2. x = 4, y = 6
Triangle TAB has a perimeter of 40 cm. Could the measures of the sides, as shown, actually represent the measures of the sides of a triangle? Justify your answer.
Answer:
NO
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. And this MUST true for ALL combinations
12 +8 IS NOT greater than 20
4x +2x+2 +x+3 = 40
7x +5=40
7x =3 5
x=5
side 4x = 20
side x+3 = 8
side 2x+2 = 12
20 +8 is bigger than 12
20+12 is bigger than 8
12 + 8 IS NOT BIGGER than 20 (it's just the same)
Simplify the expression x^5 •x^7?
How many ways can a dozen books be placed on four distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter (ie. if Book 1 is to the left of Book 2, that is different from if Book 1 is to the right of Book 2)
Answer:
217945728000 ways
Step-by-step explanation:
Given
[tex]Books = 12[/tex] --- 1 dozen
[tex]Shelf = 4[/tex]
The given condition implies that;
[tex]Book\ 1 = 4[/tex] ---- any of the 4 shelves
[tex]Book\ 2 = 5[/tex] --- any of the 4 shelves and either ways of book 1
[tex]Book\ 3 = 6[/tex] --- any of the 4 shelves and either ways of book 1 and 2
-----------------------
----------------
----------
[tex]Book\ 12 = 15[/tex]So, the number of ways is:
[tex]Ways = 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15[/tex]
[tex]Ways = 217945728000[/tex]
Compare the value of the 3 in 340, 500 to the value of the 3 in 3,160,000
Which statement is true?
Answer:
C.
Step-by-step explanation:
find the area of the triangle ! be sure to include the correct unit with the answer. (yd) , (yd2) , (yd3) .
HELP PLEASE ! i really need it . thank you
Answer:
70 yd²
Step-by-step explanation:
Area of triangle = (1/2)(base)(perpendicular height)
= (1/2)(20)(7)
= 70 yd²
NO LINKS/FLIES PLEASE .
Morgan pays $25 in monthly fees for her baseball team's uniforms and field rental. What kind of expense is the fee she pays?
A. Variable
B. Income
C. Fixed
D. This would not be an expense.
Please help I’m stuck
Answer:
96
Step-by-step explanation:
Its a pattern :) BTW can you help with mine please