can someone derive f(x) = x using first principles method. Like I know the answer is 1 and can do it by power rule but i cannot get that answer for the life of me using first principles method.

fyi first principles function is in the pic

Can Someone Derive F(x) = X Using First Principles Method. Like I Know The Answer Is 1 And Can Do It

Answers

Answer 1

The derivation by definition of f(x) = x, that is, f'(x) = 1, is found in this problem.

How to find the derivative of function f(x) by the definition?

The derivative is given by:

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h}[/tex]

For this problem, we have that:

f(x) = x.f(x + h) = x + h.

Hence:

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} \frac{x + h - x}{h}[/tex]

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} \frac{h}{h}[/tex]

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} 1[/tex]

The limit of a constant is the constant, hence f'(x) = 1.

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Related Questions

3. Find the circumference of the circle. Use 3.14 for the value of . Round your answer to the nearest tenth. 64.1 in 63.4 in 19.9 in 62.8 in 20 in​

Answers

Answer:

62.8 in

Step-by-step explanation:

The circumference, C.  of a circle with diameter d is given by the formula

[tex]C = \pi d[/tex]

Here  [tex]\pi = 3.14[/tex] and [tex]d = 20[/tex] in

So circumference = 3.14 x 20 = 62.8 inches

If Andrew's batting average is exactly 0.400 going into the series, and that value is based on exactly 2000 career hits out of 5000 previous times at bat, what is the least his average could possibly be when he
goes up to bat the tenth time of the series?

Answers

The least Andrew's average could possibly be when he goes up to bat the tenth time of the series is 0.399.

Here, we are given that,

Andrew's batting average = 0.400

Number of career hits for 0.400 batting average = 2000

Previous bat times for 0.400 batting average = 5,000

Now,

For the least possible average, he must have zero career hits in every match he bats.

Before the tenth time of the series, he will bat in 9 times

He must have 0 career hits in these 9 matches he bats in

therefore,

The total number of career hits = 2000

Total number of bat times = 5,000 + 9 = 5,009

Hence,

Average = (Total career hits) ÷ (Total number of times he bats)

= 2000 ÷ 5,009

= 0.399

Thus, the least his average could possibly be when he goes up to bat the tenth time of the series is 0.399.

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Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 25 cakes. You cannot have more than 10 chocolate cakes. Write a system of inequalities to model this system. Let x be the number of vanilla cakes and y be the number of chocolate cakes.

Answers

The inequalities are x + y <= 15 and y <= 10.

How to express the inequality?

It should be noted that inequality are used to how the relationship between expressions that are unequal.

Let x = the number of vanilla cakes.

Let y = the number of chocolate cakes.

They need at most 25 cakes. This will be x + y <= 15.

They cannot have more than 10 chocolate cakes. This will be:

y <= 10.

Therefore, the inequalities are x + y <= 15 and y <= 10.

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Figure A is a scale image of Figure B.

What is the value of x?

FAST!!! 20 POINTS AND THE BRAINLIEST FOR THE FIRST CORRECT ANSWER

Answers

Answer:

21

Step-by-step explanation:

If A 45 translates to be 35, then x can be given by (35×27)÷45 =21

How do you solve for x if x/5 = 7/3

Answers

We get that, the value of x is 11.67 when the equation is x / 5 = 7 / 3.

An equation is a combination of two expressions connected by an equal sign.

We are given an equation:

x / 5 = 7 / 3

We need to find the value of x.

Multiply both sides by 5

x / 5  × 5 = 7 / 3 × 5

x = 35 / 3

Now, we will divide 35 by 3 and round off the result to two decimal places:

x = 11.67

Therefore, we get that, the value of x is 11.67 when the equation is x / 5 = 7 / 3.

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Please show work, and brainliest will be yours.

Answers

I think the answer is: Every Sunday, you jog.
The error that my classmate made was that they should have switched the order around.

24. m/PQT if m/PQR = 25° and m/RQT = 11°.
m

Answers

13 degrees mPQT = 1 degree in internal angle .

An illustration of an internal angle?

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three interior angles. Interior angles are sometimes defined as "angles enclosed in the interior region of two parallel lines when they are intersected by a transversal."

mPQR=25 degrees , mRQT=11 degrees.

mPQT=PQR-RQT

MPQT=25-11=13 degrees

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por que es nesesario expresar un numero mixto como 1 fraccion impropia?

Answers

Es preciso transformar un número mixto en una fracción impropia cuando se requiere calcular la cantidad asociada al número en formato decimal.

¿Qué es un número mixto y una fracción impropia?

En esta pregunta vamos a abordar dos tipos de notación utilizadas entre los números racionales, esto es, números reales de la forma m / n, donde m y n son números enteros y n es distinto de cero.

Tanto los números mixtos como las fracciones impropias son utilizadas para representar números reales mayores que 1, cuyas diferencias se enumeran a continuación:

El número mixto emplea tanto números enteros como fracciones, es de hecho la suma de un número entero y una fracción. (i.e. 1.5 = 1 1 / 2)La fracción impropia es solamente una fracción, en la cual el valor del numerador es mayor que el valor del denominador. (i.e. 1.5 = 3 /  2)

Es preciso transformar un número mixto en una fracción impropia cuando se requiere calcular la cantidad asociada al número en formato decimal.

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Consider the line y=
1
2x+2.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?

Answers

If the equation of a line is [y = (12x + 2)], then the slope of a line parallel to this line will be (Tan θ = 12) and, slope of a line perpendicular to this line will be [Tan θ = [tex](\frac{-1\1}{12})[/tex]].

As per question statement, the equation of a line is [y = (12x + 2)].

We are required to find out the slope of a line parallel to this line and the slope of a line perpendicular to this line.

To solve this question, firstly, we need to know about the standard equation of a line which goes as [tex][y = (mx +c)][/tex] where, "m" is the slope of the line and "c" is the y-intercept.

Comparing our given equation [tex][y = (12x +2)][/tex] with the above mentioned standard equation of [tex][y = (mx +c)][/tex], we get (m = 12) and (c = 2).

Hence, slope of our concerned line is 12. And since slopes of all parallel lines are equal, therefore, the slope of any line parallel to the line [tex][y = (12x +2)][/tex] will be 12 or (Tan θ = 12).

Also, we know that, the product of the slopes of two perpendicular lines, (say m₁ and m₂) is equal to (-1), i.e., [m₁*m₂ = (-1)].

Therefore, the line perpendicular to [tex][y = (12x +2)][/tex] will have a slope of [tex](\frac{-1}{m})[/tex], i.e., ([tex]\frac{-1}{12}[/tex]).

Equation: An equation is a mathematical statement that consists of two separate expressions, connected by an equal signSlope: Slope of a line is defined as the inclination of the line along the positive (x- axis) and is calculated by the formula [tex][m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}} ][/tex] where (x₁, y₁) and (x₂, y₂) are two points on the line.

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2,094.1 nearest tenth

Answers

Answer:

The possible answer i giot when solving was: 2094.1

when rounded to the nearest tenth.

(4x+5)+(-5x-1) help me solve this I’m struggling

Answers

Answer:[tex]-x+4[/tex]

Step-by-step explanation:

Combine like terms:

[tex](4x+-5x)+(5+-1)[/tex]

[tex]= -x+4[/tex]

Use f (x) = |x|

f (x) is shifted left 5 and shifted up 2 to create g(x). Write the equation g(x)

Answers

Assuming that f(x)=x, we need to shift f(x) to the left by 5 and up by 2 in order to get g. (x). The equation g(x) may be written in mathematical terms as

G(x)=(x+5)+2

This is further explained below.

What is a function?

Generally, In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.

In conclusion, Assuming f(x)=x, f (x) is shifted left 5 and shifted up 2 to create g(x).  the equation g(x) is mathematically given as

G(x)=(x+5)+2

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In which of these pairs of numbers is 2 greater than the first and less than the second? 2.1, 2.3 2, 2 2.7, 3 2 , 2

Answers

Answer: most likely 2,2 I believe

Step-by-step explanation:

describe the translation from figure A to figure B

Answers

Answer:

The figure A is translated from the third quadrant to the second quadrant thus the formula used is P(x,y) = T(a,b) = Image of P(x+a, y+b). The object A and its image B are congruent and the direction and magnitude of the displacements are given by the direction and magnitude of translation vector t = ( a,b ). Where, a is the horizontal displacement ( along x-axis ) and b is the vertical displacement ( along y-axis ).

The image below has the following translation: (x, y) → (x +4, y - 1)

Determine the ordered pair for F' after the translation.

a. F' (-1, 3)

b. F' (-9, 5)

c. F' (8, -6)

d. F' (4, -1)

Answers

Check out the attached photo

Jade is stranded downtown with only $10 to get home. Taxis cost $0.75 per mile, but there is an additional $2.35 "hire" charge. Write a formula and use it to calculate how many miles Jade can travel with her money.

Answers

10=0.75x + 2.35

She starts with 10 dollars and when she get a taxi they will charge 0.75 per mile (x) and this will add a 2.35 fee at the end

If we solve for x formula ends as:
X=(10-2.35)/0.75

3. Mr. Brown bought some new shoes for $76.34. If he paid with $100 bill, how much change did he get?


please explain in number form and as little as possible but still explaining​

Answers

Answer:

23.66

Step-by-step explanation:

you just subtract the two.

100.00 - 76.34 = 23.66


Find the missing side length, s.
help!!

Answers

Answer:

The missing side length is 11.

Step-by-step explanation:

On the smaller figure the AB side is 6 and on the bigger figure the XY side  is 9. There was an increase of 3 so that means there will be an increase of 3 on  the XZ side compaered to the AC sdie witch is 8. 8 + 3 = 11.

Which number produces an irrational number when added to 1/3

Answers

Answer: 2pi thats all the answer is

Step-by-step explanation:

i dont have one just enjoy the answer, brainliest please

Sheila is baking cookies. The radius of each cookie is 4 centimeters.
What is the circumference of each cookie (use 3.14 for pi and round to
the nearest tenth)?

Answers

The circumference of each cookie is 25 cm.

Circumference is usually referred to the outer length of a circle.

If 'r' is the radius of a circle, then the circumference of the circle is given by 2πr, where π = 3.14.

Here, the radius of the each cookie, r = 4 cm

Then the circumference of each cookie = 2πr

                                                                  = 2 x 3.14 x 4

                                                                  = 25.12

                                                                  = 25 cm  

[Rounding to the nearest tenth, as 1 and 2 are less than 5, 25.12 will be 25]

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455 miles traveled in 7 hours find the unit rate

Answers

Answer:

Step-by-step explanation:

This is a fraction equal to

455 miles ÷ 7 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 7

455 miles ÷ 7

7 hours ÷ 7

=

65 miles

1 hour

=

65 miles

hour

= 65 miles per hour

Please help 2 questions with details and work out please

Answers

From properties of parallel lines the value of the indicated angle is 84° and the value of x is 4°.

Parallel lines are two lines that are equidistant from one another.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross.A line that intersects both the parallel lines is called a transversal.A set of angles on the inner side of each of the two lines but on the opposing sides of the transversal are known as alternate interior angles.Alternate external angles are those outside the two lines that the transversal is intersecting.

For the question 7 the two lines are parallel and the indicated angle is an alternate interior angle to the given angle. Hence the indicated angle is also 84°.

For question 8, the two angles are alternate exterior angles.

Hence they are equal. Therefore we can write a linear equation in x to solve for x.

21x+6=90

or, 21x=84

or, x=4°

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The sum of a number and 7 is less than 15

Answers

n = the number

The words translate into algebra as

n + 7 < 15

Subtract 7 from both sides to find n.

n = 15 - 7 = 8

Hi ~

I need help please...

I know this is a simple question.

but- I just want to know if someone can solve this without cheating at all... and make into your own words.

[tex]\rightarrow{\sf{{What \: is \: -26x \: - \: 12 \: = 15?[/tex]

Thanks~

Answers

Answer:

x would equal -1.03(1 DP)

"-26x - 12 = 15, solve for x."

Step-by-step explanation:

Start with adding 12 to both sides of the expression. Sides were switched purposely.

[tex]15 + 12 = -26x - 12 + 12[/tex]

Next, simplify your addition process. You do this by using a specific rule.

[tex](-a) = a\:\:\mathrm{if\:a\neq 0}\\-26x = 26x\\26 + (x)\\= 26 + 1\\= 27\\= -26x=27[/tex]

Lastly, we are going to divide both sides by -26(x was cancelled).

[tex]\frac{-26x}{-26}=\frac{27}{-26}[/tex]

Thus,

[tex]x= -1.03[/tex]

➲ Hope this helps, address any concerns if needed.

Answer:

x = -1.038

Step-by-step explanation:

- 26x - 12 = 15

- 26x = 15 + 12

- 26x = 27

x = - 27/26

x = - 1.038

__________

hope this helps!

A parking lot has 65 spaces total. If 30 of the spaces have cars in them, what is the ratio of empty spaces to filled spaces?

Answers

Answer: 35:30, because 65-30 equals 35 and if you do the empty spaces which there are 35 to the filled spaces which there are 30 it will become your answer of 35:30.

Hope this helps!

The solution is 7 : 6

The ratio of proportion of the empty spaces to the filled spaces is 7 : 6

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the total number of parking spaces be = P

The value of P = 65 spaces

Now , the number of spaces that are filled with cars = 30 spaces

So , the remaining number of spaces = the empty spaces

The remaining number of spaces = total number of parking spaces - number of spaces that are filled with cars

Substituting the values in the equation , we get

The remaining number of spaces = 65 - 30

The remaining number of spaces = 35 spaces are empty

Now , the ratio of empty spaces to filled spaces is given by

Ratio of empty spaces to filled spaces = 35 : 30

On simplifying , we get

Ratio of empty spaces to filled spaces = 7 : 6

Therefore , the proportion is 7 : 6

Hence , The ratio of the empty spaces to the filled spaces is 7 : 6

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Debbie has 340 dimes in three boxes. she says that there are 4 times as many dimes in the first box as in the second and 3 times as many in the third box as in the first how much money in dollars does she have in each box

Answers

The amount of money in the first box is 8 dollars

The amount of money in the second box is 2 dollars

The amount of money in the third box is 24 dollars

Solving equations

From the question, we are to determine how much money there are in each box

From the given information,

"Debbie has 340 dimes in three boxes"

Let x represents the number of dimes in the first box

y represent the number of dimes in the second box

and z represent the number of dimes in the third box

Thus,

x + y + z = 340

Also, from the given information

"she says that there are 4 times as many dimes in the first box as in the second"

x = 4y

and

"3 times as many in the third box as in the first"

z = 3x

Substitute the second and third equations into the first equation

x + y + z = 340

4y + y + 3x = 340

4y + y + 3(4y) = 340

4y + y + 12y = 340

17y = 340

y = 340/17

y = 20

Substitute the value of y into the second equation

x = 4y

x = 4(20)

x = 80

Substitute the value of x into the third equation

z = 3x

z = 3(80)

z = 240

Thus,

There are 80 dimes in the first box

80 dimes = 8 dollars

There are 20 dimes in the second box

20 dimes = 2 dollars

There are 240 dimes in the third box

240 dimes = 24 dollars

Hence,

The amount of money in the first box is 8 dollars

The amount of money in the second box is 2 dollars

The amount of money in the third box is 24 dollars

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Which of the following is NOT a voluntary response sample?
***
Choose the correct answer below.
A. A local dentist asks her patients to fill out a questionnaire and mail it back to determine the quality of the care received during an office
visit.
B. Quiz scores from a college level statistics course are analyzed to determine student progress.
C. A radio station asks for call-in responses to a question concerning city recycling.
OD. A survey is taken at a mall by asking passersby if they will fill out the survey.

Answers

Of the given options, the one that is NOT a voluntary response sample is B. Quiz scores from a college level statistics course are analyzed to determine student progress.

What is a voluntary response sample?

A voluntary response sample refers to a sampling method where those who are to be in the sample are asked to be in the sample. They will have a choice on accepting the offer to be in the sample.

When quiz scores from a college level statistics course are used as the sample, this is not a voluntary response sample as the students who had the scores were not consulted.

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The complement of an angle is 90 degrees less than the supplement of the angle. What is the angle?

Answers

The angle which is as described in the task content is; .

Complementary and Supplementary angles

If we assume the angle in discuss is; x.

It's complement is therefore; (90-x).

Therefore, since the complement of the angle is 90° less than the supplement; we have;

90 - x = 180 - 90

90 - x = 90

x = 0°

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Which of the following represents the area of a rectangle whose length is 5x − 3 and whose width is x + 7?

Answers

I believe the answer is 5x2 + 32x -21

Find The Value Of X.

Answers

Answer:

X=25.5

Step-by-step explanation:

First we need to apply supplementary angles.

We see that angle EGH is 78 degrees. Since Angle BEC falls on the same line as EGH we can easily calculate the Angle for BEC

Supplementary angles add up to 180. 78+x=180

180-78 is 102

4x=102

divide both sides by 4

x=25.5

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