-) Use the E -& definition of a limit to prove thatlim 7x3 = 4x-1

The [tex]\lim_{x \to 1} 7x-3=7(1)-3=4[/tex] using the definition of a limit.The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.The limit of f(x) at x = c is L according to the epsilon-delta definition of limits if > 0 there'sa > 0 such that if the distance of x from c is less than, then the distance of f(x) from L is less than . The idea that we can approach L as closely as we like is expressed in this way.[tex]\lim_{x \to a}f(x)= L[/tex] if > 0, > 00 < | x a| < | f(x) L | < Now, consider the limit[tex]\lim_{x \to 1} 7x-3=4[/tex]Here, f(x) = 7x - 3, a = 1, L = 4Proof: > 0, = > 00 < | x - 1 | < | 7x - 3 - 4 | = | x - 1 | < = Hence, [tex]\lim_{x \to 1} 7x-3=4[/tex]Learn more about epsilon-delta here:https://brainly.com/question/27322217#SPJ9

Mathematics College

-) Use the E -
& definition of a limit to prove that
lim 7x3 = 4
x-1

Answers

Answer 1

The $\lim_{x \to 1} 7x-3=7(1)-3=4$ using the ε − δ definition of a limit.

The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

The limit of f(x) at x = c is L according to the epsilon-delta definition of limits if ε > 0 there's a δ > 0 such that if the distance of x from c is less than, then the distance of f(x) from L is less than ε. The idea that we can approach L as closely as we like is expressed in this way.

$\lim_{x \to a}f(x)= L$ if ∀ ε > 0, ∃ δ > 0

0 < | x − a| < δ

⇒ | f(x) − L | < ε

Now, consider the limit

$\lim_{x \to 1} 7x-3=4$

Here, f(x) = 7x - 3, a = 1, L = 4

Proof:

∀ ε > 0, ∃ δ = ε > 0

0 < | x - 1 | < δ

⇒ | 7x - 3 - 4 | = | x - 1 | < δ = ε

Hence, $\lim_{x \to 1} 7x-3=4$

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Related Questions

Please help me bro.

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Answer:

Step-by-step explanation:

GIVEAWAY TO GET 100 POINTS + BRIANLIEST IF YOU ANSWER WHATS 9+10 B)

Answers

Answer:

uhhh 21

Step-by-step explanation:

Solve using substitution.

y = –6
–8x − 7y = –6

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Okay so you put -6 in where y is then solve and youll get your answer

-8x-7(-6)=-6

What is the equation of the line that passes through the point (2,3) and has a slope that is undefined?

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Answer:

x=2

Step-by-step explanation:

An undefined slope is the slope of a vertical line.

line through (2,3) is y=mx+b

Answer: x=2

whats the slope and the y-intercept of the graph of y−6=38x

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slope is 38 and y intercept is -6

Any one know how to do this?

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Answer:

10.33

Step-by-step explanation:

mean = (6+13+4+15+17+7) / 6 = 62/6 = 10.33

Which of the following properties describes the mathematical expression?
7 + 2 = 2 + 7

A. Associative

B. Distributive

C. Identity

D. Commutative

Answers

Answer:

Identity

Step-by-step explanation:

7+2=2+7

is an identity

Which of the following are geometric sequences? Select all correct answers.

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Answer:

A, B, E

Step-by-step explanation:

Notice that A, B, and E all maintain their common ratios, while C and D do not.

Which of the following is the closest estimate to the value of n? 223÷72=n

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Answer:

121

Step-by-step explanation:

A figure including triangle RNB is shown.

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This is how to solve it, I believe this is correct. If you need a better understanding, let me know.

Right awnsers only brainlest and points I know if you’re lyin just giving away points !

Answers

Answer:

1/13

Step-by-step explanation:

4/52 =1/13

the 4 is number of Jack cards and the 52 is the total number of cards

During July in Jacksonville florida

Answers

Answer:

yo i live in florida

Step-by-step explanation:

Paula made this model to show the sum of two mixed numbers. Write the addition equation shown by the model and solve it.

You can write out the fraction names or use the forward slash (/) on your keyboard to represent the fraction bars.

A number line from zero to one partitioned into thirds. There is a gray rectangle above the number line stretching from zero to three and two thirds. To the right is a darker gray rectangle above the number line stretching from three and two thirds to six and one third.

Your answer:

Answers

Answer:

$3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}$

Step-by-step explanation:

Given

See attachment for number line

Required

Determine the model

From the attachment, we can see that each partition is 1/3

The gray rectangle covers 11 partitions.

So:

$Gray = 11 * \frac{1}{3}$

$Gray = \frac{11}{3}$

Express as a mixed number

$Gray = 3\frac{2}{3}$

The black rectangle covers 8 partitions

So:

$Black= 8 * \frac{1}{3}$

$Black= \frac{8}{3}$

Express as a mixed number

$Black= 2\frac{2}{3}$

So, the model is:

$Gray + Black = Total$

Where Total is the point where the black rectangle stops

$3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}$

Paula made this model to show the sum of two mixed numbers. Write the addition equation shown by the

can someone answer real quick

Answers

Answer:− -19s

Step-by-step explanation:

Move

PLSSS HELP!! Ty whoever helped me! :) Question: Select the statement that is true about the two-dimensional figure.

A quadrilateral with the vertices labeled L, M, N and O. Angles M L O and L M N are greater than 90 degrees, and angles L O N and M N O are less than 90 degrees.

∠LMN is an acute angle.
∠LMN is an obtuse angle.
∠MNO is an obtuse angle.
∠MNO is a right angle.

Answers

Answer: Choice B

∠LMN is an obtuse angle.

==========================================

Explanation

Let's go through the answer choices to see which are true, and which are false.

A. This is false. It is stated that "LMN is greater than 90 degrees", so this angle is obtuse. Acute angles are less than 90 degrees.B. This is true. See choice A above.C. This is false. We're told that "angle MNO is less than 90 degrees". That makes the angle acute. D. This is false. See choice C above. Right angles are 90 degrees exactly. Often a small square marker is used to denote a 90 degree angle.

Choose all options that apply. Which of the following are equal to 20%? | a) .25 b) 1/5 Oc) 1/10 d) .20

Answers

Answer:

b and d

Step-by-step explanation:

b because 1/5=20 out 100% and d because 20. and go to the left 2 spaces which I feel like you have 2 answers

Answer:

b, d

Step-by-step explanation:

0.25 x 100 = 25%

1/5 = 0.20 = 20%

1/10 = 0.10 = 10%

0.20 x 100 = 20%

Adair suggests that they package together the fries and soda in a combo for a $0.75 discount. lf the student council pays $0.85 per trench fry and $1.20 per soda, then how much money will they make if they sell 45 combos? (french fries cost $3.50 and soda costs $2.30 normally)

Please answer I will give you the brainliest!

Answers

Answer:

$58.50

Step-by-step explanation:

It is given that the student council pays

For per french fry = $0.85

For per soda fry = $1.20

Discount on the combo of fries and soda = $0.75

Total revenue for one combo = $0.85 + $1.20 - $0.75 = $1.30

Since the total revenue for one combo is $1.30, therefore the total revenue for 45 combo is

Total revenue for 45 combo = 45 × $1.30 = $58.50

Therefore, they will make $58.50 if they sell 45 combos.

Answer:

13 :)

Step-by-step explanation:

Please help I need the answer quick this assignment is almost due!

Answers

the correct answer is x= -3

Answer:

x = -3

Step-by-step explanation:

The two angles shown are corresponding angles, meaning that they have the same value. Because of this, we can create an equation to solve for the value of x.

2x + 9 = 7x + 24

Remember, those two angles are similar, and that's why we can make the two values equal to each other. First, let's remove 7x from both sides.

2x - 7x + 9 = 7x - 7x + 24

-5x + 9 = 24

Then, we'll remove 9 from both sides.

-5x + 9 - 9 = 24 - 9

-5x = 15

Finally, we'll divide both sides by -5 to isolate x and figure out what it is equivalent to.

-5x/-5 = 15/-5

x = -3

And there it is... the value of x. Hopefully that's helpful! :)

a. Write an inequality that represents the numbers that are not solutions of x+3.8>11.3 .
Inequality:
Question 2
b. Graph the inequality from part (a).

Answers

Inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.

What are the various operators used in inequalities for comparison?

The various operators used in inequalities for expression are -

greater than - ' > 'less than - ' < 'greater than or equal to - ' ≥ 'less than or equal to - ' ≤ '

Given is a inequality in one variable which is → x + 3.8 > 11.3.

PART - A

The inequality that represents the coordinates that are not the solutions of this inequality is -

x + 3.8 < 11.3

we can simplify it to get -

Subtract 3.8 from both sides -

x + 3.8 - 3.8 < 11.3 - 3.8

x < 7.5

PART - B

In order to plot the graph of this inequality, firstly we will plot the line of equation -

x = 7.5.

Since, the inequality is strict, make a dashed line to represent the equation.

Take the coordinates of origin O(0,0), and substitute it in the inequality -

0 < 7.5

which is true. Therefore, we will shade the complete side where origin lies.

The graph of the inequality is plotted an attached with the answer.

Therefore, inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.

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a. Write an inequality that represents the numbers that are not solutions of x+3.8>11.3 .Inequality:

y=7-4x/|2x+5|+3 Find the domain

brainliest to the fastest answer

Answers

The domain of the function is all set of real numbers except -2.5

How to find the domain of the function?

The equation of the function is given as:

y = 7 - 4x/|2x + 5| + 3

Set the denominator of the fraction to 0

So, we have

|2x + 5| = 0

Remove the absolute value bracket

So, we have

2x + 5 = 0

Subtract 5 from both sides of the equation

So, we have

2x = -5

Divide both sides of the equation by 2

So, we have

x = -2.5

Hence, the domain of the function is all set of real numbers except -2.5

Answers

The value of x is 5

Define the term Similar triangles?

Triangles with the same shape but different sizes are said to be similar triangles. To be more specific, two triangles are comparable if their respective sides are proportionate and their corresponding angles are congruent.

Two triangles are similar if corresponding angles are congruent and corresponding sides are proportional.

from the below figure, both the triangles are similar, ∆ABC ≈ ∆EFB

By using Thales's theorem, the ratio of the sides of triangles are;

BE/EA = BF/FC

15/30 = x/10

x = 5

Therefore the value of x is 5

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The ratio of triangle sides can be calculated using Thales' theory, and it is the value of x is 5

Define the term Similar triangles?

Similar triangles are those with the same shape but varying sizes. To be more precise, two triangles are comparable if their matching angles and respective sides are congruent.

If matching sides are proportional and corresponding angles are congruent, two triangles are similar.

Both triangles in the following figure are comparable ∆ABC ≈ ∆EFB

The ratio of triangle sides can be calculated using Thales' theory, and it is;

BE/EA = BF/FC

15/30 = x/10

x = 5

Therefore the value of x is 5

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(fractions 5th grade) 3/9 + 2/3

Answers

Answer:

Step-by-step explanation:

Simplify 3/9 by 3 -> 1/3

Now that both fractions have the same denominator, you can add them.

1/3 + 2/3 = 3/3 or 1

Please answer the question in the picturee

Answers

Answer: 8

Step-by-step explanation:

12-4= 8

*8 is the length of the side because of this theory I forgot, but yeah!

Your friend was bored one day and started making patterns using Cheerios from a new box he had opened. He laid the Cheerios on the table as such:
Based on the two images above and the information about the box, answer the following questions.
A) Identify and label the variable
B) Make a table for up to 8-figure patterns
C) Write an equation to represent the nth term of the sequence.
D) If the pattern continues, what figure number will have 20 whole Cheerios in it?
E) Is it reasonable to think this pattern would continue forever? If not, explain.
F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

PLS ANSWER ALL OF THE QUESTIONSSS I REALLY NEED THE ANSWERS ASAPPPPPPP PLEASE AND THANK YOU

Answers

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1 1

2 3

3 6

4 10

5 15

6 21

7 28

8 36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1 1

2 3

3 6

4 10

5 15

6 21

7 28

8 36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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Choose the answer.
A(n) __________ is a rate that has a denominator of 1.

Question 12 options:

empty set

contradiction

identity

unit rate

Answers

Answer:

Unit Rate

Step-by-step explanation:

Unit Rate measures every quantity by a single unit of measurement. For example, 1 foot is the unit rate in '12 inches / 1 foot' since 1 foot=12 inches.

what fraction of a semicircle is an angle that measures 11pi/18 radians? express your answer as a fraction in simplest terms

Answers

Check the picture below.

let's recall that, the arc made from 0 to π is just half a circle or namely a semi-circle, so any fraction of π refers to that arc

$\cfrac{11\pi }{18}\qquad \textit{really means}\qquad \cfrac{11}{18}\qquad \textit{of that semi-circle}$

$what fraction of a semicircle is an angle that measures 11pi/18 radians? express your answer as a fraction$

Ellie and Jordan went to the store where packs of gum cost 85¢ each and candy bars cost 60¢ each. They spent $15.00 and brought 4 more packages of gum than candy bars. How many packages of gum did they buy?

Answers

Answer:

they bought 8 candy bars and 8 + 4 = 12 packs of gum.

Step-by-step explanation:

Let's use algebra to solve this problem:

Let x be the number of candy bars they bought.

Then, the number of packs of gum they bought is x + 4.

The total cost of the candy bars is 60x cents.

The total cost of the packs of gum is 85(x + 4) cents.

We know that they spent $15.00, which is 1500 cents, so we can write an equation:

60x + 85(x + 4) = 1500

Simplifying the equation, we get:

145x + 340 = 1500

145x = 1160

x = 8

Therefore, they bought 8 candy bars and 8 + 4 = 12 packs of gum

Answer: 22

Step-by-step explanation:

The number of the gum is 13 and the number of the candy will be 22.

What is linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.

They spent $26.38 total and bought 35 items total.

Let x be the number of the gum and y be the number of the candy.

Then the equation will be

x + y = 35 ...1

0.54x + 0.88y = 26.38 ...2

By solving the equations 1 and 2, then we have

x = 13 and y = 22

Then the number of the gum is 13 and the number of the candy will be 22.

a number has the same digits in its hundreds place and it’s hundrthes place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place

Answers

In a case whereby a number has the same digits in its hundreds place and it’s hundredths place the number of times that the value is greater in the hundreds place than the value of the digit in the hundreds place is 10,000 times.

How can the value of the digit can be calculated?

The question can be interpreted that the particular number has the same digit which is seen in hundreds place hence hundredths place.

we can then represent the digit as '1'.

The value of number's hundreds place can be represented as 100

we can as well represent the number's hundredths place as 0.01

the number of times the value of the hundreds place digit exceeds the value of the hundredths place digit can be expressed as 100/0.01 =(100*100)/1 = 10, 000

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missing options:

A. 100,00

B. 100

C. 1,000

D. 10,000

FInd the measure of the arc using the picture provided , please and thanks

Answers

The measure of arc angle QTP is 204 degrees.

How to find arc angle?

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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Indicate whether the sentence or statement is true or false. (2 + 3) + 5 = 2 + (3 + 5)

Answers

Answer:

True

Step-by-step explanation:

(2 + 3) + 5 = 2 + (3 + 5)

5+5=2+8

10=10

this statement is true

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which of the following is an example of menu pricing? group of answer choices a resort selling different vacation packages (economy, comfort, luxury) at different prices. all of the answers are examples of menu pricing. one or two firms sell complementary products together. costco sells a 16 pack of bar soap. define a pendulum with example(s), describe the type of motion, provide a brief discussion of the physics (can include formulas), and comment on the similarities and differences between a pendulum motion and a spring motion. Can someone help me ASAP its due tomorrow. I will give brainliest if its all done correctly. Answer part a, b, and c for brainliest!! HELP ASAP 100 points as i need answer soonYou join Mountain Water Co an expanding bottled water company as an information security officer. The company wants to do a lot of advertising of its bottled water products through its website. The CEO asks you to review the company website and report if it is secure. After talking to the webmaster you find out the following:The Web server accepts all connectionsNo authentication is requiredSelf-registration is allowedThe web server is connected to the InternetIs the situation secure? Select all that apply.a. Yes. There is no threat to a bottled water company so it is secure.b. There is insufficient information available to answer this question.c. No. Anything that is connected to the Internet is insecure.d. No. The system is allowing everyone to register. Only individuals who are associated with the company should be able to register.e. No. If there is no authentication, then anyone with access to the website online can access it. For good security only individuals with certain authorized roles should access a website. Many times in today's society is critiqued for being lazy. Is it? Why or why not? Could you have shown the same determination that Braddock did to succeed? Explain. the pistachio, pistacia vera, a member of the cashew family, is a small tree originating from central asia and the middle east. the tree produces seeds that are widely consumed as food. if a pistachio cell that contains 30 chromosomes undergoes mitosis, how many chromosomes will each of the two new cells have? a government in which the people vote firsthand? If u were signing papers and it asks u "does applicant identity as transgender" what would that mean? Also what is a social security number? solve the system by using elementary row operations on the equations. follow the systematic elimination procedure. x1 3x2 Choose TWO of the stories or poems from this semester. In two ACES paragraphs, explain how each of the selections you choose reflects something that is uniquely American.1. The celebrated jumping frog of Calaveras county by mark twain2. Experts from William Bradfords journal of Plymouth Plantation by William Bradford3. Equianos autobiography by Equiano4. Common sense by Thomas Paine5. Declaration of Independence by Thomas Jefferson6. The Masque of the red death by Edgar Allan Poe7. The wife of his youth by Charles W.C HesnuttPlease Help me with this Essay... I'm trying to finish my homework so I can go to sleep. I am giving 100 points and marking the Brainleist to the first person who answers this. Please and thank you in advance. I truly appreciate it! What number is equal to 580 tenths and 17 thousandths? 580.017 58.017 5.817 0.5817 Describe the flexor and extensor muscles of the cat forelimb Stacy had difficulty choosing her puppy from the group of wiggling pups.Which of the following is a prepositional phrase from the sentence above? A. from the group B. had difficulty C. wiggling pups D. choosing her puppy On the grid above, flag F is rotated around point S. Which of the images does NOT result from this transformation? A. image 3 B. image 2 C. image 1 D. All of the images result from this transformation. alex is pushing a heavy box.The force he exerts is represented by the white arrow. In order to make his task easier in which direction should an additional force be applied? help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!! In American society, we often formalize norms by writing them down in some kind of a code (such as the criminal code.) These norms are then called: What are the three types of technological data? which factor does not account for the strong loyalist sentiment prevalent throughout georgia during the revolutionary war? the kinetic energy of a falling ball changes from 20 joules to 80 joules. during this time, how much work did the force of gravity transfer to the ball?

-) Use the E - & definition of a limit to prove that lim 7x3 = 4 x-1

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-) Use the E -
& definition of a limit to prove that
lim 7x3 = 4
x-1