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

In the equation -3x - 9.6 = 20, what is the coefficient?


A. 20

B. -9.6

C. -3

D. -3x

Answers

Answer:

x=-3

Step-by-step explanation:

a wheel makes 20 revolutions per min. how many revolutions does it make per second? type and integer or simplified fraction.

Answers

Answer:
1/3
Step by step:
Since the wheel is rotating at 20 revolutions per minute, to find the amount of rev’s per second would go as follows:

20/min = ?/second

convert each denominator to numerical form referring to seconds

20/60 = ?/1

Simplify

1/3 = ?/1

Find value of ?

1/3 = (1/3)/1

Simplify both sides completely

1/3 = 1/3

1/3

Answer:

1200 revolutions per second

Step-by-step explanation:

60 seconds per minute so multiply 60 x 20 to get 1,200

Please complete this question, the question is saying: write the correct integer in the blank


Is due please. I will give brainlest

Answers

First one is negative 3 then its negative 3 over 6

Find the cos of angle T....

Answers

Answer:

C = 24/25

Step-by-step explanation:

Recall, CAH.

Thus:

Cos T = adjacent/hypotenuse

Reference angle = T

Adjacent = 24

Hypotenuse = 25

Therefore,

Cos T = 24/25

Plz help me solve this!!-

Amy drove her hoverboard 3 miles in 40 minutes. Jim hopped 2 miles in 20 minutes. Who traveled at a greater average speed? Define an appropriate unit of speed and provide mathematical justification for your answer

Answers

Answer:

Amy traveled at 4.5 mph, while Jim traveled at 6 mph. Therefore, Jim traveled at a greater average speed.

Step-by-step explanation:

Given that Amy drove her hoverboard 3 miles in 40 minutes, while Jim hopped 2 miles in 20 minutes, to determine who traveled at a greater average speed, the following calculation must be performed:

(3/40) x 60 = Amy's speed

0.075 x 60 = Amy's speed

4.5 = Amy's speed

So Amy traveled 4.5 miles per hour.

(2/20) x 60 = Jim's speed

0.1 x 60 = Jim's velocity

6 = Jim's speed

Instead, Jim traveled 6 miles per hour.

Therefore, Jim was the one who traveled at a greater average speed.

Select the correct answer.
What is the LCM of the numbers 3, 6, and 9?

A.
9
B.
18
C.
36
D.
54

Answers

Answer:

D

Because you have to find out what they could all equal up to

Answer:

d

Step-by-step explanation:

5, 7, 9
Show that the mean of these three numbers is 7.​

Answers

Answer:

Mean= 7

Step-by-step explanation:

The numbers are 5, 7, 9

Mean= sum of numbers/ total numbers

= 5+7+9/3

= 21/3

= 7

Hence the mean is 7

If our school has about 300 seventh graders, about how many would be expect to watch 4 to
8 hours of television weekly?
A. 55
B. 116
C. 138
D. 165

Answers

Answer:

55

Step-by-step explanation:

X+y=15-2x+5y=-2 solve your systems of solutions and record your answer as an ordered pair

Answers

Answer:

x = 11 and y = 4

Step-by-step explanation:

Given equations are :

x+y=15 ...(1)

-2x+5y=-2 ...(2)

We need to solve the systems of equations.

Multiply equation (1) by 2.

2x+2y=30 ...(3)

Adding equation (2) and (3).

-2x+5y+2x+2y = -2+30

7y = 28

y = 4

Put the value of y in equation (1).

x+4=15

x = 11

So, the solution of the given equations are x = 11 and y = 4.

Dario puts 44 marbles in a box in which 14 are red, 12 are blue, and 18 are yellow. If Dario picks one marble at random, what is the probability that he selects a red marble or a yellow marble?

Answers

Answer:

not simplified: 18/44    

Simplified: 9/22

Step-by-step explanation:

Julie bought 12
packages of cucumber seeds. Each bag contains 42
seeds. If she plants half of the seeds, how many of the
seeds does she have left?

Answers

Answer:

12x42=504

504/2=252

252

Step-by-step explanation:

Simplify completely
[tex] \frac{2x - 24}{8} [/tex]
A)
[tex] \frac{x - 24}{4} [/tex]
[tex] \frac{x - 12}{4} [/tex]
C) 2x-3
D) x-3​

Answers

Hopes this helps:

Answer: A) x-24/4

One-seventh of a number, increased by twelve

Answers

Answer:

one seventh of 14 increased by 12 is 14

Step-by-step explanation:

so my example will use 14, so one seventh of 14 is 14 divided by 7 which is 2 then you just add 12 to 2 which gets you 14

An expression is defined as a set of numbers, variables, and mathematical operations. The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "One-seventh of a number, increased by twelve" can be written in the form of an expression as shown below.

One-seventh of a number → x × (1/7) = x/7One-seventh of a number, increased by twelve→ x/7 + 12

Hence, The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.

Learn more about Expression here:

https://brainly.com/question/13947055

#SPJ2

Please help me i am taking a test and i really need help

Answers

Answer:

31.4159in

Step-by-step explanation:

Answer:

31.4

Step-by-step explanation:

You bought some stock, and then the stock price went down by 17.2% from the purchase price. By what percentage would the price have to increase for the investment to be back to the original value?

Answers

Step-by-step explanation:

Let's pick some easy numbers for illustration.

Let x equal our initial stock purchase, and, say it was $100.

x = $100

The problem says it's value dropped by 17.2%. If x = 100 is 100% of our stock value the 17.2% less is

[tex]x - 0.172x = 0.828x[/tex]

So now our stock is worth 0.828(100) = $82.80.

Now how much of an increase do we need to get back to $100.

[tex]100 - 82.80 = 17.20[/tex]

So our base is $82.80 because our stock price dropped, we want to know what percent increase is $17.20 of $82.80

[tex]17.20 \div 82.80 = 0.2077[/tex]

Or 20.77% increase to get back to original price.

To make this generic, since $100 is not supplied information, substitute x for 100 and 0.828x for the amount of money dropped.

x = original stock value

[tex]x - 0.828x [/tex]

Is the amount of value lost, and to be regained in the second part of the question.

To find out what portion the decrease is of the new value

[tex] \frac{(x - 0.828x)}{0.828x} = \frac{0.172x}{0.828x} = 0.2077 [/tex]

Or 20.77%

I see you already received your answer, hope tomorrow goes an excellent route :)

a. How many 1/3s are in 2 2/3?​

Answers

Answer:

1 2/3 = (1•3+2)/3 = 5/3. Therefore, 5/3 ÷ 1/3. = 5.

Step-by-step explanation:

So the answer is 5.

the answer indeed is 5 :)) step by step

Add. Express the sum as a fraction in simplest form. −1/3+1/2 The sum is

Answers

Answer:

1/6

Step-by-step explanation:

The value of 2^0 ??

Answers

Answer:

1

Step-by-step explanation:

. It is read as 2 raised to zero. Now let see how to solve such problem For example 3^5 then it means 3×3×3×3×3 = 243 Now back to question Anything raised to zero is always 1 Hence 2^0= 1

Simplify the following:
(3i-3)(3i+3) and (4i+7)(-6i+20)

Answers

Answer:
1. -18
2. 164+38i

Please answer these in a fraction form. Thank you have an AMAZING day!

1. 2/5 ÷ 3 1/10 = ?
2. 4 1/3 ÷ 4/7 = ?
3. 3 1/6 ÷ 9/10 = ?
4. 5/8 ÷ 2 7/12= ?​

Answers

Answer:

use Photomath app to answer your question.

Can someone please help me

Answers

Answer:

A) 23cm.

B) 32.0625 square cm.

Step-by-step explanation:

Perimeter: Just add all the sides together like so:

4.75x2 + 6.75x2 = 23cm.

Area: Multiply the base and height together:

4.75 x 6.75 = 32.0625 square cm.

23cm

4.75 + 4.75 = 9.50

6.75 + 6.75 = 13.50

13.50 + 9.50 = 23.00

If f(x) = 9x-8, which of the following is the inverse of f(x)?
O A. f'(x) = *19
O B. f'(x) = x;
O c. f-'(x) = 48
X-9
O D. f-1(x) =
8

Answers

f(x) = 9x+8
y = 9x+8
x = 8y + 9
x-9 = 8y

x-9
----- = y
8

f-¹ =
x-9
------
8

The circumference of a circle measures 11.277 ft.
What is the measure of the diameter of this circle?

Answers

Answer:

3.590ft

Step-by-step explanation:

We know what the circumference of the circle is, and we need to find its diameter. Therefore, we need to find an equation that links the two together.

Well, what comes to mind is the fact that the circumeference, [tex]c[/tex], is equal to [tex]\pi[/tex] multiplied by the diameter, [tex]d[/tex]. We can express this like so:

[tex]c = \pi d[/tex].

In this scenario, we know what [tex]c[/tex] is, so we need to rearrange the formula to make [tex]d[/tex] the subject. Dividing both sides by [tex]\pi[/tex] will accomplish this, and gives us:

[tex]\frac{c}{\pi} = d[/tex].

So if we divide the circumference by [tex]\pi[/tex], we will find the diamater. Well,

[tex]\frac{11.277}{\pi} = 3.58958...[/tex]

and so to 3 decimal places we get the answer

[tex]d = 3.590\text{ft}[/tex].

What is the solution to the inequality below?
−8m ≥ 40

Answers

divide each term by -8 and simplify

2. m < -5

Question 2 What is the correct order of operations to complete a math problem?​

Answers

Parentheses,(brackets etc.) Exponent, Multiply/divide doesn’t matter which one. Addition/ subtraction. Doesn’t matter which one. You can remember this with the abbreviation PEMDAS. Please mark Brainliest!!!

VERY QUICK HELP!!!! A toy pyramid has the dimensions shown below. The base of the pyramid is an equilateral triangle. What is the surface area of this pyramid?

Answers

Answer: 102cm²

Step-by-step explanation:

Area of base = 6 × 7 ÷ 2 = 21

Area of lateral face = 6 × 9 ÷ 2 = 27

Since all of the sides of the base are equal, we can multiply the area of 1 lateral face by 3 to get the area of all the lateral faces.

27 × 3 = 81.

Now we add up the area of the base and the lateral faces.

21 + 81 = 102cm²

I am not a professional, simply using prior knowledge!

Note- It would mean the world to me if you could mark me brainliest!

At a University, 72% of courses have a final exam, 46% of courses require a final paper, and 32% of courses have a final exam and require a final paper. What is the probability that a randomly selected course at this University requires a final exam or a final paper

Answers

Look at the picture attached

-3m + 5>26
How to answer this question

Answers

9514 1404 393

Answer:

  m < -7

Step-by-step explanation:

Maybe you want to find the value of m.

Subtract 5, then divide by -3.

  -3m +5 > 26 . . . given

  -3m > 21 . . . . . . subtract 5 from both sides

  m < -7 . . . . . . . . divide by -3. Dividing by a negative number reverses the inequality.

A garden table and a bench cost $903 combined. The garden table costs $53 more than the bench. What is the cost of the bench?

Answers

2x+53=903-53
2x=850 divide by two
x=425
bench - $425

Forty percent of all high school graduate work during the summer to earn money for college tuition for the upcoming fall term. Assuming a binomial distribution, if 6 graduates are selected at random, what is the probability that none of the graduates have a summer job

Answers

Answer:

[tex]0.0467[/tex] is the probability that none of the graduates have a summer job

Step-by-step explanation:

Here

P [tex]= 0.40[/tex] and n [tex]= 6[/tex]

Probability that none of the graduate gets job

this means that x = 0

P (x = 0) [tex]= ^6C_0 * (0.40)^0 * (0.60)^6[/tex]

P (x = 0) [tex]= 0.0467[/tex]

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