Given the function f(x) = [tex]\frac{|x|}{x}[/tex] , find [tex]\lim_{x \to \00^-} f(x) and \lim_{x \to \00^+} f(x) and \lim_{x \to \00} f(x)[/tex]

Answers

Answer 1

Answer:

[tex]\displaystyle \lim_{x \to 0^-} f(x) = -1 \\ \lim_{x \to 0^+} f(x) = 1 \\ \lim_{x \to 0} f(x) = DNE[/tex]

General Formulas and Concepts:

Algebra I

Graphing FunctionsFunction Notation

Calculus

Limits

Evaluating Limits GraphicallyIf [tex]\displaystyle \lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)[/tex], then [tex]\displaystyle \lim_{x \to a} f(x)[/tex] exists

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle f(x) = \frac{|x|}{x}[/tex]

Step 2: Graph/Evaluate

Graph the function so we can evaluate the given limits. See attachment.

We see from the function that when we approach 0 from the left, we will get a -1.

∴ [tex]\displaystyle \lim_{x \to 0^-} f(x) = -1[/tex]

We see from the function that when we approach 0 from the right, we will get a 1.

∴ [tex]\displaystyle \lim_{x \to 0^+} f(x) = 1[/tex]

Since the limit from the left does not equal the limit from the right, the limit as x approaches 0 of f(x) does not exist (DNE).

Given The Function F(x) = [tex]\frac{|x|}{x}[/tex] , Find [tex]\lim_{x \to \00^-} F(x) And \lim_{x \to

Related Questions

Which statement is true based on the graph ?

Answers

Answer:

C: The speed increases from A to F

Step-by-step explanation:

Check each node A to F including A and F.

B is higher than A, C is higher than B, ...

This is true for all of them, so it is increasing.

The speed of the car is increasing in the time interval from point A to point F. Option C is correct.

What is speed?

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

What is the graph?

The graph depicts the relationship between the x and y axes through the use of curves.

Here,
The graph shows the speed and time relation of the car,
Where,
The speed of the car is increasing from A to F,
The speed of the car is decreasing from F to G,
The speed of the car is increasing from G to H,
The speed of the car is decreasing from H to K,

Thus, the car's speed increases over the time span from point A to point F. Option C is the right answer.

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Multiply and divide decimals.
One pound of chocolate chip cookies cost $3.79. David buys exactly 5 pounds of chocolate chip cookies. How much will the cookies cost?
State Your answer. Give Details. Explain what you did and justify Your steps.
And also, you'll get brain if u do these directions. :)

Answers

Answer:

5 pounds of chocolate chip cookies cost $18.95.

Step-by-step explanation:

If one pound of chocolate chip cookies cost $3.79, then 5 pounds of chocolate chip cookies will cost 3.79 times 5 dollars, which is equal to $18.95.

Hope this helps!

1/2x5/6, as a fraction, because my brain is not remembering rn

Answers

Answer:

5/12

Step-by-step explanation:

5/12

you just multiply the numerators and the denominators

WILL GIVE BRAINLIEST TO CORRECT ANSWER!!!

The perimeter of a triangle is 63 in. The longest side is 12 in. longer than the medium side, and the medium side is 6 in. more than the shortest side. Find the length of each side of the triangle?

1. longest side is?
2. medium side is?
3. shortest side is?​

Answers

Answer:

1.13

2.19

3.31

Step-by-step explanation:

Let the length of the shortest side be a.

a+a+6+a+6+12=63

3a=39

a=13

Simply
x + 50 × 10 = 150​

Answers

Answer:

x + 50 × 10 = 150

x+500=150

x=150-500=-350

Step-by-step explanation:

solution,

here,

given,

x+50*10 = 150

or, x+500=150

or, x= 150 -500

therefore, x= -350

hope this helps u..

If f(x) = x3+ x2and g(x) = x4+ x2+ x, what is the value of f(x) –g(x) when x = 1?
A) -2
B) -1
C) 1
D) 5

Answers

Answer:

B) -1

Step-by-step explanation:

[tex]f(x)=x^3+x^2\\\\g(x)=x^4+x^2+x[/tex]

METHOD 1

[tex]f(x)-g(x)=(x^3+x^2)-(x^4+x^2+x)=x^3+x^2-x^4-x^2-x\\\\=-x^4+x^3-x\\\\x=1\\\\-1^4+1^3-1=-1+1-1=-1[/tex]

METHOD 2

[tex]x=1\\\\f(1)=1^3+1^2=1+1=2\\\\g(1)=1^4+1^2+1=1+1+1=3\\\\f(1)-g(1)=2-3=-1[/tex]

Write a classification essay to describe two types of animal flight​

Answers

Do pidgins and eagles

One of the two basic types of animal locomotion: powered flight, actual flight, or gliding. Real wings are only found in most bird species, most insect orders, and bats.

What are the categories?

A category listing is a list of various product categories, such as children's clothing, women's clothing, and men's clothing. Any form of a category can be simply created

Soaring and gravitational gliding are two distinct types of gliding flight.

In controlled gravitational gliding, a creature propels itself in a precise direction after delaying its descent and relying on the wind for horizontal motion (parachuting).

Adaptations for guided gliding are primarily made to increase glide ratio (the amount of horizontal distance covered per unit descent)

Therefore, powered flight or true flight are the two basic categories of animal locomotion.

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Question 4 Given that P = 6 and a 2, which yields a quotient greater than -9? O A 3 B 3() c Зр (-2) (-p) (-3)​

Answers

Answer:

I think is A or B I don't know

Answer:

a

Step-by-step explanation:

Kamala has 2 liter of soup. he pours it into 4 bowls. each bowl gets an equal amount. how many millilitres of soup are in each bowl?​

Answers

Answer:

500ml

Step-by-step explanation:

[tex]2000 \div 4 = 500[/tex]

Answer:

500 ml

Step-by-step explanation:

2 litres= 2000 millilitres divided into 4 bowls=2000÷4=500 millilitres

The price of Stock A at 9 A.M. was ​$12.21. Since​ then, the price has been increasing at the rate of ​$0.11 each hour. At noon the price of Stock B was ​$12.71. It begins to decrease at the rate of ​$0.15 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answers

Answer:

mildiu usa so lapuaña kqyiq iwguiq oga oga. apphq. kgaoa

Step-by-step explanation:

suost. oaabqj the ksysa

There were 70 wings at the Super Bowl party. I ate 14. What percent of the wings did I devour?

Answers

Answer: omg yes I ate like 10 wings last night. Your answer should be 20

Step-by-step explanation:

Solve the system of linear equations by elimination. 8x-5y=11 4x-3y=5

Answers

Answer:

(x,y)= ( 5 over 273, - 265 over 273)

Step-by-step explanation:

After solving the obtained equation with the elimination method the obtained value of x and y will be 2 and 1 respectively.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that,

8x-5y=11  ------ (1)

4x-3y=5 --------- (2)

In order to solve the above equation with the elimination method, we have to apply the multiplicative distribution law as,

Multiply by 2 in equation 2

2(4x-3y=5)

8x- 6y = 10  ----- (3)

Subtract equation 3 from equation 1,

(8x- 6y)-(8x-5y) = 10 - 11

8x-8x-6y+5y = -1

-y = -1

y=1

Substitute the value of y in any of the equations 1  to get the value of x

8x-5y=11

8x-5(1)=11

8x-5=11

8x=16

x=2

Thus, after solving the obtained equation with the elimination method the obtained value of x and y will be 2 and 1 respectively.

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Write -√-49 as an imaginary number using i.
Represent 4-3i on the graph

Answers

- /-49
-/-1 * 7 * 7
-7i

4 - 3i
Go to 4 on the x axis (right)
Go to -3i on the y axis (down)
Your coordinate is (4, -3i)

To graph -3i, it is like 0 - 3i
Your coordinate is (0, -3i)

The rectangle can be made into a hollow cylinder with height 40cm and radius 1.910cm.
a) calculate the volume of this cylinder.

Answers

Answer:

458.45 cm³

Step-by-step explanation:

Volume of a cylinder is A = πr²h.

A = π(1.910)²(40)

A = 458.43 cm³

Use the drop down menus to complete the statement to match the information shown by the graph

Answers

Answer:

yes ikow

Step-by-step explanation:

you can do that if you want to buy

Answer:

where the graph?

Step-by-step explanation:

what is the area of this tile?

10in

8in

6in

Answers

Answer: I can give you the volume: 480. But to find the area I need more context to know which are the length and width.

all vertical and horizontal cross-sections of any Cube are all the same size and shape what about vertical and horizontal cross-sections of a pyramid are they all the same size are they all the same shape discuss why or why not​

Answers

Answer:

All the horizontal sections are the same shape like their base, but have different sizes.

All vertical sections through top are triangles, size are different.

The vertical sections not cut through top are 4 sided shapes, sizes are different.

Step-by-step explanation:

Rachel has 2/3 pound of snack mix. She eats 5/12 of the snack mix.


How much of the snack mix did Rachel eat?


Enter your answer in the box as a fraction in simplest form.


pound


Basic

Answers

Answer:

[tex]\frac{5}{18} pound of snack mix is eaten by Rachel.[/tex]

Step-by-step explanation:

Given

Total snack mix with Rachel [tex]\frac{2}{3}[/tex] Pounds

Snack mix eaten by Rachel [tex]= \frac{5}{12}[/tex] of the total snack mix

[tex]\frac{5}{12}[/tex] of the total snack mix accounts for

[tex]\frac{5}{12} * \frac{2}{3} = \frac{5}{18}[/tex] Pound

Complete the table for

y = x/4 -1

Answers

Answer:

X     Y    

0     -1

2     -0.5

4     0

6     0.5

8     1

Step-by-step explanation:

I hope i got that right

Sheila rolled a number cube numbered 1 through 6 and tossed a coin for heads, H, or tails, T.
Which list represents all the possible outcomes of rolling the numbercube and tossing the
coin?

Answers

The second one. You can roll the dice and get a number 1-6 and heads or tails.

Can someone solve this please

Answers

Answers:

11.) 0.25

12.) 3:20

13.) 0.75

14.) 19

Answer:

Question 11: 0.25

Question 12: 3:20

Question 13: 0.75

Question 14: 19

Triangle GHI is dilated to form new triangle JKL. If angle H is congruent to angle K, what other information would prove that the two triangles are similar by the capital AA similarities postulate?

Answers

Answer: Angle I is congruent to angle L

Step-by-step explanation:

Did da test

To prove ΔGHI and ΔJKL are similar following statements must be true,

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex][tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]

What are similar triangles?

"Two or more triangles are similar if and only if the corresponding angle measures same and their corresponding side lengths are in proportion.."

What is dilation?"It is a geometric transformation where there is a change in the size of an object without changing its shape.""The size of the object changes on the basis scale factor."

For given example,

ΔGHI is dilated to form new ΔJKL.

Also, angle H is congruent to angle K.

To prove ΔGHI and ΔJKL are similar.

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]

Therefore, to prove ΔGHI and ΔJKL are similar following statements must be true,

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]

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Who can help me with this

Answers

Answer:

Growth

Step-by-step explanation:

Given

[tex]\frac{2}{3}(2.5)^x[/tex]

Required

Growth or decay

The general form is:

[tex]y = ab^x[/tex]

Such that:

[tex]b = rate[/tex]

For b, we have the following conditions:

[tex]b > 1[/tex] ----- Growth

[tex]0<b <1[/tex] --- Decay

[tex]b = 1[/tex] ---- None

Compare [tex]\frac{2}{3}(2.5)^x[/tex] to [tex]y = ab^x[/tex]

[tex]b = 2.5[/tex]

Because 2.5 > 1, then the first condition applies (growth)

12) Find the zeros of the function:
f(x) = x2 + 5x – 36
IS

Answers

Answer:

x² +5x - 36

= x² - 4x + 9x - 36

= x(x - 4) +9(x - 4)

= (x - 4) (x+9)

so x = 4, - 9

f one Canadian dollar is equivalent to US$0.8150, how much do you need in

Canadian funds to buy US$800.00? (2 ma​

Answers

Answer:

It will take $ 989.59 in Canadian funds to buy $ 800.

Step-by-step explanation:

If one Canadian dollar is equivalent to US $ 0.8150, in order to determine how much money is needed in Canadian funds to buy US $ 800.00 the following calculation must be performed:

0.8150 = 1

800 = X

(800 x 1) / 0.8150 = X

800 / 0.8150 = X

981.59 = X

Therefore, it will take $ 989.59 in Canadian funds to buy $ 800.

Help me with this one please

Answers

Answer:

-7

Explanation:

(-3)^2- (-4)^2 =

= 9 - 16 = -7

5. Licorice are 5 cents. How many licorice can you buy
with 10 cents?

Answers

Answer:

2

Step-by-step explanation:

5+5=10

Each licorice is 5 cents, if you have 10 cents, you’ll be able to buy 2 licorice

The force acting on a beam was measured 5 times under the same operating conditions. This process was repeated by 3 observers, resulting in 3 sets of data. The standard deviations of these data sets were: Standard Deviation 1= 1.11, Standard Deviation 2= 0.99, Standard Deviation 3= 1.15 The corresponding mean values were: 52.3, 51.5, and 52.7, respectively. Compute the Pooled Standard Deviation for these data sets. (Provide your answer using two decimal places)

Answers

Answer:

The Pooled Standard Deviation for these data sets is 1.09

Step-by-step explanation:  

Given that;

Standard Deviation 1 = 1.11

Standard Deviation 2 = 0.99

Standard Deviation 3 = 1.15

pooled standard deviation is given as;

[tex]S_{pooled}[/tex] = (n1 - 1 )s1² + ..... + ( nk - 1 )sk² / n1 + ..... + nk - 1

where n1, n2....., nk are the sample sizes of k groups and s1, s2, ....., sk are the standard deviations of k groups respectively

so for the 3 groups;

[tex]S_{pooled}[/tex]² =   (n1 - 1 )s1² + (n2 - 1 )s2² + ( n3 - 1)s3² / n1 + n2 + n3 - 3

we substitute

[tex]S_{pooled}[/tex]² =   (5 - 1 )1.11² + (5 - 1 )0.99 ² + ( 5 - 1)1.15² / 5 + 5 + 5 - 3

[tex]S_{pooled}[/tex]² =   (4.9284 + 3.9204 + 5.29) / 12

[tex]S_{pooled}[/tex]² =   14.1388 / 12

[tex]S_{pooled}[/tex]² =   1.1782

[tex]S_{pooled}[/tex] = √1.1782

[tex]S_{pooled}[/tex] = 1.08544 ≈ 1.09

Therefore, The Pooled Standard Deviation for these data sets is 1.09

A class of 195 students went on a field trip. They took 19 vehicles, some cars and some buses. If
each car holds 5 students and each bus hold 25 students, how many buses did they take?

Answers

Answer:

1car 8 bus

Step-by-step explanation:

1×5=5

8×25=190

Most Popular Last Names. In alphabetical order, the six most common last names in the United States in 2018 are Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). Assume that a sample of 50 individuals with one of these last names provided the following data:
Brown Williams Williams Williams Brown
Smith Johnson Williams Smith Miller
Johnson Williams William Johnson Jones
Miller Jones Jones Smith Smith
Miller Johnson Smith Jones Jones
Johnson Smith Brown Smith Johnson
Jones Smith Smith Williams Brown
Johnson Johnson William Smith Brown
Smith Miller Johnson Brown Johnson
Brown Jones Miller Smith Miller
Summarize the data by constructing the following:
A. Relative and percent frequency distributions
B. A bar chart
C. A pie chart
D. Based on these data, what are the three most common last names?

Answers

Answer:

Kindly check attached picture for barchart and piechart distribution

Step-by-step explanation:

Given the name data:

Name ____ freq ___R/Freq ____% frequency

Brown ____7 ______0.14 ______14

Smith ____ 12 -____ 0.24 ______24

Williams__ 8 ______0.16 ______ 16

Miller ____6 ______0.12 ______ 12

Jones ___ 7 ______ 0.14 ______ 14

Johnson _ 10 _____ 0.20 ______20

The three most popular last names are :

Smith, Johnson and Miller

Based on the information given in the bar chart, it should be noted that the most popular last names are Smith, Johnson, and Williams.

Solving the bar chart.

It should be noted that the information given in the question is used in solving the bar chart and pie chart.

The name with the least number of people is Miller. On the other hand, the most popular last names are Smith, Johnson, and Williams.

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Which pair of ratios forms a proportion?A 7 1510 18B 5 159 27C 3 1510 25 The sum of 6 times a number and 8 times another number is 12. The difference of those numbers is 9. What are the two numbers One way to get consistent, valid data is toA. be sure that instruments are calibrated properly.B. use simple instruments to make measurements.C. select the best data to place into data tables.D. make the measurements as quickly as possible. The best answer gets brainiest please help!Instructions: Convert this problem into y=mx+b formQuestion: 3x+y=0 A television assembly plant has a variable production output ranging from 200 sets to 850 sets a day. The building for both manufacturing and warehousing has an area of 80,000 square feet and is leased from a real estate firm at an annual rate of $7.95 per square foot. It employs 250 people and their wage cost is, in large part, a function of the number of televisions produced. Most of the components that go into the assembly are also produced in the plant with in-house equipment that is operated based on production requirements. The most likely example of fixed cost in this plant is ______________. Simplify completely [tex] \frac{2x - 24}{8} [/tex]A)[tex] \frac{x - 24}{4} [/tex][tex] \frac{x - 12}{4} [/tex]C) 2x-3D) x-3 Uld American Women win the fight for suffrage?A. They worked for a constitutional amendment.B. They joined the African American civil-rights movement.C. They persuaded their husbands to support the goal.D. They went on strike until their demands were met. What causes there to be a H+ ion concentration gradient to build up inside the thylakoid space? Check all that apply. a. The electrons provide energy for the H+ pump to transport more H+ ions into the thylakoid space. b. A special enzyme produces more H+ ions. c. Photons of light create more H+ ions. d. The photolysis of water releases H+ ions into the thylakoid space. the TV Margaret wants cost $270 This week only, the TV is discounted by 25%. Margaret must pay 6% sales price. which saves the most money?A. Taking the discount first then adding on the sales taxB. Adding on the sales tax first and then taking the 25% discountC. Both methods save the same amount of money What is the act of moving from one place to another A)MovingB)WakingC)RunningD)Locsmotion what happened to black tom island * Indique 4 ejemplosen los cuales aparezcaun nivel de medicion diferente What five things should you do when telling a story? The amount of calories burned depends upon the type, duration, and intensity of theactivity. There are two types of Direct Stafford Loans, the Direct Subsidized Loan andthe:A. Direct Loan Subsidy.B. Indirect Subsidized Loan.C. Direct Unsubsidized Loan.D. Indirect Unsubsidized Loan. All the stars you can see at night are still in existence. True False HELP PLSSS! WHO EVER GETS IT RIGHT WILL GET THE TOP COMMENT!!! THANK YOUUU!!! TRUE OR FALSE!! !!?? The 2020 accounting records of Skysong, Inc. reveal these transactions and events. Payment of interest $10,800 Collection of accounts receivable $189,200 Cash sales 50,900 Payment of salaries and wages 56,900 Receipt of dividend revenue 19,000 Depreciation expense 16,100 Payment of income taxes 15,700 Proceeds from sale of vehicles 12,100 Net income 38,000 Purchase of equipment for cash 21,900 Payment of accounts payable Loss on sale of vehicles 3,100 For merchandise 115,600 Payment of dividends 14,700 Payment for land 73,700 Payment of operating expenses 27,600Required:Prepare the cash flows from operating activities section using the direct method. 4/b - 1/2b = -7/4A. 7B. -2C. 0D. 2 To determine what effect the salespeople had on purchases, a department store polled 700 shoppers as to whether or not they had made a purchase and whether or not they were pleased with the service. Of those who had made a purchase, 130 were happy with the service and 119 were not. Of those who had made no purchase, 142 were happy with the service and 309 were not.Find the probability that a shopper who was happy with the service had made a purchase (round off to the nearest hundredth).