Use the definition of continuity and the properties of limits to show that the function

f(x) = x2 + 5(x - 2)7 is continuous at x = 3.

Answers

Answer 1

Answer:

Applied the definition and the limit.

They had the same result, so the function is continuous.

Step-by-step explanation:

At function f(x) is continuous at x = a if:

[tex]\lim_{x \to a} f(x) = f(a)[/tex]

In this question:

[tex]f(x) = x^{2} + 5(x-2)^{7}[/tex]

At x = 3.

[tex]\lim_{x \to 3} x^{2} + 5(x-2)^{7} = 3^{2} + 5(3-2)^{7} = 14[/tex]

[tex]f(3) = 3^{2} + 5(3-2)^{7} = 14[/tex]

Since [tex]\lim_{x \to 3} f(x) = f(3)[/tex], f(x) is continuous at x = 3.


Related Questions

Joshua and Noah go to the movie theater and purchase refreshments for their friends.

Joshua spends a total of $74.75 on 9 drinks and 4 bags of popcorn.

Noah spends a total of $18.00 on 2 drinks and 2 bags of popcorn.

Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.

Using these equations, determine and state the price of a bag of popcorn, to the nearest cent

Answers

Answer:

Formula is y=mxtb try to plug it in

Step-by-step explanation:

Formula is y=mxtb try to plug it in

1. What does this quote mean to you?

2. How can you apply it to your life?

"You exist only in what you do." ~ Federico Fellini

***Must answer with a pharagraph, minimum 5 sentences, just give me your opinion.

Answers

Answer:

My opinion is that you can exist any many things as you navigate through life. This quote is very wrong because you can exist in doing things for other people and not just yourself! You can not be selfish your entire life! I think that you should be for other people! I think that doing stuff for yourself is okay to a certain extent!

Step-by-step explanation:

THIS IS SOOO WRONG( idk tho)

This quote is telling us that you can't exist unless you are doing something worth being remembered for. Through out our lives we all listen to what the world tells us, but not many of us actually do what we want to. We live our lives for someone else, but I plan to change that. Instead of letting the public decide how I should live my life I will live for me. I will work harder in school, become smarter than my parents and grow as a person. I want to be remembered for stepping out of my comfort zone and being different. This is the year that I exist, and show people that I exist for a purpose.

Step-by-step explanation:

Went really deep with this one.

PLEASE HELP!!!!
Which choices are equivalent to the expression below? Check all that apply.
5^2 • 5^9

Answers

Answer:

D & E

The ones you chose are correct.

The value of a piece of equipment is decreasing at a rate of 7,5% yearly. If the equipment
was valued at $930 when it was purchased, which function represents the value of the
equipment x years after it was purchased? Explain,

Answers

Answer:

y=930 x 075^x

Step-by-step explanation:

y is the price after the amount of years x being plugged into the equation. 930 is what you started with. 7.5 is what is being decreased so divide that by 100 and you get 0.075 plug in the amount of years into x and you have your equation

Find two consecutive odd integers such that the sum of their squares is 202.

Answers

Answer:

9 and 11

Step-by-step explanation:

The squareroot of 202 is 14... so the numbers are both less than 14.

9*9= 81

11*11= 121

121+81= 202

Answer:

9 and 11

Step-by-step explanation:

(9^2) + (11^2) Simplify the exponents

81 + 121 = 202

Please Help.... 50 points.

Answers

Answer:

94

Step-by-step explanation:

Answer:

94 is the answer

Step-by-step explanation:

Please answer this correctly

Answers

Answer:

x =1

Step-by-step explanation:

Assuming the figures are similar, we can use ratios to solve

x        2

---- = -----

4         8

Using cross products

8x = 2*4

8x = 8

Divide by 8

8x/8 = 8/8

x=1

If a is 3 and c is 12, then 4ac equals

Answers

Answer:

144

Step-by-step explanation:

4ac=

4(3)(12)=

144

Hope this helps!

4ac= 144

Explanation:

4*a = 3 * c = 12

4*3*12 = 12* 12

= 144

Which of the following is used to name a segment that has an endpoint at point A and another endpoint at point B?

Answers

You would write AB with a horizontal line segment over the letters A and B

So you would write this [tex]\overline{AB}[/tex]

If you cannot draw that on your computer, then I would stick to saying "segment AB".

line segment is used to name a segment that has an endpoint at point A and another endpoint at point B

What is a line segment ?

A line segment is a part of line that is bounded by two distinct end points , and contains every point on the line that is in between its endpoint  .

since , in question it is given that their are two end points A and B then, it will form a line segment named AB

the answer is line segment

learn more about line segment :

https://brainly.com/question/25727583?referrer=searchResults

#SPJ2

A company that manufactures toy trains is making a new box car. To fit on the track, the smallest dimensions of the toy box car must be 2 inches. What should the length and the height of the toy if the company wants the toy box car to be geometrically similar to an actual box car with the dimensions shown?

PLEASE HELP!!!

Answers

Answer:  figures not drawn to scale a. length = 12 inches, height = 3 inches b. length = 14 inches, height = 3 inches c. length = 21 inches, height = 5 inches d. length = 37 inches, height = 5 inches reset next previous 1 next similar solids: mastery test submit test tools info all rights reserved.

Step-by-step explanation:

~Help me with this please!
I will mark as BRANLIEST!

(Look at the attachment)

Answers

Answer:

You will find the answer from my explanation.

Step-by-step explanation:

Let the cost of one small shirt be x

And that of a large shirt be y

From the expression above;

4x + 14y = 210; since the total cost of a small shirt by Wili is;

4 * x and the large shirts 14 * y

Similarly for Jordan we have:

12x + 11y = 110; since the total cost of a small shirt by Jordan is;

12 * x and the large shirts 11 * y

We now have two equations,

So you can solve both equations now using elimination method;

If you multiply all the variables of x and y in the first equation by 3 and then subtract the second equation from it, x would be eliminated remaining y;

Multiplying the first equation we have;

12x + 42y = 630

- 12x + 11y = 110

------------------------------

0. + 31y = 520

You can continue from there

how to find the scale factor of triangles

Answers

Answer:

you pick similar sides from both the triangles and try and divide or find common multiples. for ex if the sides are 3 and 9, you can find that the scale factor is 3 since 9/3 is 3

Step-by-step explanation:

Nick's science class is observing the growth rate of a tomato plant. The tomato plant grows 3 cm every week for 12 weeks. What is the total growth of the tomato plant during these 12 weeks?

Answers

Answer:

36 cm

Step-by-step explanation:

Because the plant is growing the same amount each week you would take 12(3) and get 36 cm at the end of the 12 weeks.

Divide. 21,382.62 ÷ 10,000

Answers

The answer is: 2.138262

Answer:

the answer is 2.138262

Step-by-step explanation:

hope this helps

What is the area of the shape below

Answers

Answer:

The answer is 886.

You need to find the area of each specific shape and then add them together.

19 * 11 = 209, which is the area of the rectangle in the middle.

34 * 16 = 544, which is the area of the rectangle on the bottom of all the other shapes.

Now the triangle is a little more complicated. It only gives you the length of both the triangle and the rectangle combined, so first you need to subtract the length of the rectangle.

25 - 11 = 14, which is the length of the triangle.

Next, to find the area of a triangle, you need to multiple the length times the height and then divide it by two. 14 * 19 = 266. Divide 266 by 2 and you get 133.

Now, like I said earlier, add all of these together.

544 + 209 + 133 = 886.

estion



Carmen, Goran, and Henry have a total of

$

127


in their wallets. Henry has

4


times what Goran has. Carmen has

$

7


more than Goran. How much does each have?

Answers

Answer:

Carmen is $ 27, Henry is $ 80, and Goran is $ 20.

Step-by-step explanation:

be Carmen's money "c", Goran's "g" and Henry's "h"

Now, we organize the equations and we are left with:

c + g + h = 127

h = 4 * g

c = g + 7

replacing in the main one we have:

g + 7 + g + 4 * g = 127

6 * g = 127 - 7

g = 120/6

g = 20

now replacing:

h = 4 * 20 = 80

c = 20 + 7 = 27

therefore, Carmen is $ 27, Henry is $ 80, and Goran is $ 20.

Isaiah receives $10 per week for his allowance. let m be the total amount
of money Isaiah gets and let w be the number of weeks he receives his
allowance. Which variable is the dependent variable?

A: W; number of weeks
B: M; total amount of money

Answers

B: M; total amount of money

Step-by-step explanation:

because the time is a independent variable

Answer:

b id the answer

Step-by-step explanation:

becasue i just finished my test

Identify the design of the following study. A researcher classifies students according to three parental income groups and also according to three possible score ranges on the SAT examination. He randomly selects two students from each of the nine (Income, SAT) combinations. The researcher records the grade point averages (GPA) of those sample members at the end of the sophomore year.

a. Randomized block design
b. Two-Factor ANOVA with replication
c. One-way ANOVA

Answers

Answer:

140000000

Step-by-step explanation:

Carol is a pet groomer whose yearly gross pay is $45,000. Her exemptions total $4,000 and the state tax rate is 3.5%. How much does she pay in state taxes each month?

Answers

Answer:

  $119.58

Step-by-step explanation:

We expect Carol's annual tax bill to be the difference of her pay and exemption, multiplied by the tax rate:

  annual tax = ($45,000 -4,000) × 0.035 = $1,435

Then her monthly tax bill will be 1/12 of this:

  monthly state tax = $1435/12 = $119.58

Carol pays $119.58 in state taxes each month.

What is the reason called when you switch sides of an equation?

Answers

Answer:

Possibly Symmetric Property?

Step-by-step explanation:

Answer:

PSP maybe?

Step-by-step explanation:

What is the circumference of a circle with a radius of 91 mm? (use 22/7 for pi; show your work in numbers)

Answers

Answer:

571.77 is the correct answer because

C=2πr=2·π·91≈571.76986

A debate team consists of five girls and four boys. (Everyone is distinguishable.) How many ways can they stand in line, so that at least two of the girls are standing next to each other?

Answers

Answer:

9!-2880 = 360000.

Step-by-step explanation:

If p represents “a number is divisible by 2,” q represents “a number is odd,” and r represents “a number is even,” what does this statement imply?

WILL MARK BRAINLIEST!!!!

Answers

Answer:

B

Step-by-step explanation:

idk y but still ur teacher can't do anything

In an insect colony, there are 270 insects after 7 days. If there were initially 80 insects, how long will it take the population to grow to 700 insects?

Answers

Step-by-step explanation:

Total insects = 270

Days = 7

If 80 insects to 700 insects

Days = 700 ÷ 80 = 8.75

It will take 8.75 days

Identify the type of regression that returns the equation y = x^2 + 7x - 15.
A. linear
B. quadratic
C. exponential
D. power

Answers

Answer:

  B.  quadratic

Step-by-step explanation:

The equation y=x^2+7x-15 is a quadratic equation. It might be the result of a quadratic regression.

_____

The descriptors "linear," "quadratic," "exponential," and "power" describe the sort of equation that is used to try to match the data. Quadratic regression returns a quadratic equation.

A piece of equipment costs $50,000 new, but depreciates 15% per year in each succeeding year.
Find its value after 10 years.

Answers

Answer:

-$25,000

Step-by-step explanation:

15% of $50,000 is $7,500 Therefore..

10 x $7,500 = $75,000 ( 10 being the amount of years and 7500 being the 15% )

$50,000 - $75,000 = -$25,000

Hope this helps!!

-Conrad

The probability that Rahul succeeds at any given free-throw is 70%, percent. He was curious how many free-throws he can expect to succeed in a sample of 15 free-throws.

He simulated 30 samples of 15 free-throws where each free-throw had a 0.7, probability of being successful.

Rahul counted how many free-throws were successful in each simulated sample. Here are his results:

(picture attached)

Use his results to estimate the probability that he succeeds at 11 or fewer free-throws in a sample of 15 free-throws. Give your answer as either a fraction or a decimal.

P(11 or fewer sucessess) =

Answers

Answer:

0.2

Step-by-step explanation:

i took the test on khan academy :D

The probability of the number of times from the result that he got 11 or fewer free throws is; P(11 or fewer sucessess) = 0.2

How to find probability of success?

We are told that he simulated 30 samples. From the dot plot, we can see how many times he got 10 free throws, 11 free throws, 12 free throws, 13 free throws, 14 free throws, 15 free throws.

Now, from the dot plot, the number of times that he had 11 or fewer free throw successes is 6 times.

Thus;

P(11 or fewer sucessess) = 6/30

P(11 or fewer sucessess) = 1/5

P(11 or fewer sucessess) = 0.2

Read more about Probability at; https://brainly.com/question/25870256

If you can buy 6 bulbs of elephant garlic for $18 then how many can you buy with $54?

Answers

Answer:

18 bulbs for $54

Step-by-step explanation:

if we get 6 bulbs for $18

we can keep going

12 bulbs for $36

18 bulbs for $54

or we can divide 54 by 18 and get 3

then we multiply 3 by 6 and get 18 bulbs :)

if im correct may i please get brainliest

Answer:

18 bulbs

Step-by-step explanation:

let x number of bulbs can be bought for $54.

[tex]\frac{6}{18} =\frac{x}{54} \\\frac{1}{3} =\frac{x}{54} \\\\3x = 54\\x =\frac{54}{3} \\x=18[/tex]

what is the distance between -45 and -98 on a number line

Answers

Answer:

53

Step-by-step explanation:

53 units because from 45 to 98 is 53 spaces

An online retailer has determined that the average time for credit card transactions to be electronically approved is 1.8 seconds. (Round your answers to three decimal places.) (a) Use an exponential density function to find the probability that a customer waits less than a second for credit card approval. (b) Find the probability that a customer waits more than 3 seconds. (c) What is the minimum approval time for the slowest 5% of transactions

Answers

Answer:

a) 0.426 = 42.6% probability that a customer waits less than a second for credit card approval.

b) 0.189 = 18.9% probability that a customer waits more than 3 seconds.

c) The minimum approval time for the slowest 5% of transactions is 5.39 seconds.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

An online retailer has determined that the average time for credit card transactions to be electronically approved is 1.8 seconds.

This means that [tex]m = 1.8, \mu = \frac{1}{1.8} = 0.5555[/tex]

(a) Use an exponential density function to find the probability that a customer waits less than a second for credit card approval.

This is [tex]P(X \leq 1)[/tex].

[tex]P(X \leq 1) = 1 - e^{-0.5555*1} = 0.426[/tex]

0.426 = 42.6% probability that a customer waits less than a second for credit card approval.

(b) Find the probability that a customer waits more than 3 seconds.

This is P(X > 3).

[tex]P(X > x) = 1 - P(X \leq 3) = 1 - (1 - e^{-0.5555*3}) = 0.189[/tex]

0.189 = 18.9% probability that a customer waits more than 3 seconds.

(c) What is the minimum approval time for the slowest 5% of transactions

This is x for which [tex]P(X \leq x) = 0.95[/tex]

So

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

[tex]0.95 = 1 - e^{-0.5555x}[/tex]

[tex]e^{-0.5555x} = 0.05[/tex]

[tex]\ln{e^{-0.5555x}} = \ln{0.05}[/tex]

[tex]-0.5555x = \ln{0.05}[/tex]

[tex]x = -\frac{\ln{0.05}}{0.5555}[/tex]

[tex]x = 5.39[/tex]

The minimum approval time for the slowest 5% of transactions is 5.39 seconds.

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