Find the indicated limit, if it exists.
The limit is approaching 5.

Possible Options:
a) 0
b) 8
c) 3
d) The limit does not exist​

Find The Indicated Limit, If It Exists. The Limit Is Approaching 5.Possible Options:a) 0b) 8c) 3d) The

Answers

Answer 1

Answer:

d) The limit does not exist

General Formulas and Concepts:

Calculus

Limits

Right-Side Limit:                                                                                             [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Left-Side Limit:                                                                                               [tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Step-by-step explanation:

*Note:

In order for a limit to exist, the right-side and left-side limits must equal each other.

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}[/tex]

Step 2: Find Right-Side Limit

Substitute in function [Limit]:                                                                         [tex]\displaystyle \lim_{x \to 5^+} 5 - x[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]:                           [tex]\displaystyle \lim_{x \to 5^+} 5 - x = 5 - 5 = 0[/tex]

Step 3: Find Left-Side Limit

Substitute in function [Limit]:                                                                         [tex]\displaystyle \lim_{x \to 5^-} x + 3[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]:                           [tex]\displaystyle \lim_{x \to 5^+} x + 3 = 5 + 3 = 8[/tex]

∴ Since  [tex]\displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)[/tex]  , then  [tex]\displaystyle \lim_{x \to 5} f(x) = DNE[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits


Related Questions

Find the exact value of the​ following, without using a calculator.

Answers

9514 1404 393

Answer:

  (√17 -4√595)/102

Step-by-step explanation:

To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.

  sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle

  cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6

  sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle

  cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17

The sum of angles formula is ...

  sin(α+β) = sin(α)cos(β) +cos(α)sin(β)

So, our sine is ...

  [tex]\sin\left(\sin^{-1}\left(\dfrac{1}{6}\right)+\tan^{-1}(-4)\right)=\dfrac{1}{6}\cdot\dfrac{1}{\sqrt{17}}+\dfrac{\sqrt{35}}{6}\cdot\dfrac{-4}{\sqrt{17}}\\\\=\dfrac{1-4\sqrt{35}}{6\sqrt{17}}=\boxed{\dfrac{\sqrt{17}-4\sqrt{595}}{102}}[/tex]

need help ASAP !! A line segment has endpoints(3,14) and (3,22) which of the following statements is true?

Answers

Answer:

the answer is b. the segment has a length of 8 units vertical.

Step-by-step explanation:

please answer this as quick as possible.​

Answers

Answer:

False

x=8-10=-2

Step-by-step explanation:

[tex]\sf\purple{False.}[/tex] ✅Step-by-step explanation:-

[tex]10 = x - 8 \\ ➡ \: x = 10 + 8 \\ ➡ \: x = 18[/tex]

[tex]\sf\red{The\:value\:of\:x\:is\:18.\:}[/tex]

[tex]\sf\pink{Hence,\:it\:is\:false.}[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Solve x3 + x2 - x - 1 =. 0 by factoring by grouping

Answers

Answer:

(x^2-1)(x+1)=0

(x+1)(x-1)(x+1)=0

x=1; x=-1

Step-by-step explanation:

Answer:

(x^2-1)(x+1)=0

(x+1)(x-1)(x+1)=0

x=1; x=-1

Step-by-step explanation:

Move words to the blanks to make the sentence true. HELPP ME FASTTT PLEASEEE

Answers

filling, three-dimensional, unit squares

I hope this helps ^^

Answer:

Covering

two dimensional

unit squares

Step-by-step explanation:

Hope this helps! Sorry if incorrect

Alexis surveys a random sample of 80 students at his school and finds that 22 of them
usually walk to school. There are 1,760 students at the school. Predict the number of
students who usually walk to school.

Answers

Answer:

484 students

Step-by-step explanation:

This is simple probability. Assuming 22/80 students walk to school within a small population, and there are 1760 students at the school, there should be (22/80)*1760 students that walk to school in total. (This is just theoretical). This is 484 students.

The number of students who usually walk to school will be 484 students.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Alexis surveys a random sample of 80 students at his school and finds that 22 of them usually walk to school.

Then the number of students who usually walk to school will be

⇒ 22 / 80

⇒ 11 / 40

We know that the ratio will remain the same.

There are 1,760 students at the school.

Let x be the number of students who usually walk to school.

Then the number of students who usually walk to school will be

x / 1760 = 11 / 40

x = 484 students

Thus, the number of students who usually walk to school will be 484 students.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

What’s the correct answer I will mark as brainlest ASAP

Answers

Answer:

9

Step-by-step explanation:

240x.70=168 left after 30% to teacher

168/2=84 left after putting half in jar

25 students x 3=75 given to students

84-75=9 left

Which of the following graphs is the graph of a linear function?

Answers

Answer:

A is the answer

Step-by-step explanation:

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and plans to construct a 95% confidence interval for the mean, using an SRS of 16 bags. Suppose he is not sure if the distribution of net weights is Normal. In which of the following circumstances would he not be safe to use a t procedure?
A. A boxplot of the data has multiple large outliers.
B. The mean and median of the data are nearly equal.
C. The sample standard deviation is large.
D. A boxplot of the data shows a very slight skew.

Answers

Answer:

A. A boxplot of the  data has multiple large outliers.

D. A boxplot of the data shows a very slight skew.

Step-by-step explanation:

A) The normal distribution does not have outliers. The outliers are any point outside the 3σ interval which 99.7% of the data. The 0.3% data would not be outliers.

B) YEs the mean and median of the normal distribution are nearly equal. AS it is asymmetrical.

C) When the sample standard deviation is large the data is spread about the mean. The normal distribution  is flatter and wider

D) The normal distribution is never skewed.If one end is longer then the distribution is not assymmetric and the normal distribution asymmetric meaning half is the mirror reflection of the other half.

So A and D indicate circumstances where he not be safe to use a t procedure.

multiply 6kg25g by 8​

Answers

48kg200g....…........

Answer:

(6*1000)g+25g=6025g

6025g*8=48200g

48kg200g. {:1000g=1kg}

a house purchased for 170828 is worth $73828 after 12 years. assuming that the house's value depreciated the same amount from year to year, what was it worth at the end of the year 4? Round to the nearest cent.​

Answers

Answer:

After four years the house was worth $128,891.03

Step-by-step explanation:

170828(x)^12 = 73828

solve for x

x = 0.932 (House depreciates by 6.8% yearly)

plug in x and change into function and substitute 4 for 12 because it's 4 years

170828(0.932)^4

128891.0334

Answer:

Match the packaging type with the number of seedlings it contains.

gerbera daisy cell pack

gerbera daisy flat

standard flat

standard cell pack

Step-by-step explanation:

poop I don't know what to do-

Answers

Me either ive been stuck on a question and no one will help me

Answer:

me three

Step-by-step explanation:

you guys are awesome

HEPL MEE, I NEED EXTREME HELP!

Find the area and the perimeter of this shape!!!!
SEE ATTACHED FILE.

Answers

Answer:

A= ( 5 x 3 ) x [(9-5)x3 divided by 2]

15+6

=21

P= 5+5+3+9

=22

Calvin wrote inequalities to compare the heights, in feet, of rivers above or below flood stage.
Select all of the inequalities that are correct.
A. -10 > -9
B. 1> -18
C. -25 > -30
D. 3 < -5
E. -10 < 3

Answers

Answer:

I'm not 100% sure but I think its B. 1> -18

Help ASAP will give brainly 9th grade math

Answers

Answer: 14. 2z + 3yz - 6z +2yz + y - z - 4y 2z - 6z  -4z - z -5z + 3yz + 2yz + y - 4y  3yz + 2yz -5z + 5yz + y - 4y Answer = -5z + 5yz - 3y  15. -4ab + 3ax + ba - 6xa -4ab + ba Answer = -5ab - 3xa  16. -c(3b - 7a) -3bc - 7ac   Step-by-step explanation: Hopes this helps. Mark as brainlest plz!

how to solve this equation​

Answers

So see what number or fraction or something that makes that number = that number

A fair die is rolled twice. What is the probability that each roll shows an odd number? (show work)

Answers

Answer:

1/4

Step-by-step explanation:

To find probability, multiply the probability of one roll times the probability of the second roll.

A die usually have 6 numbers so ill assume it has that.

1/2 or 3/6 of the sides are odd. So multiply 1/2*1/2 to get 1/4.

A train travels 18 kilometers in 12 minutes. At this rate, how far does the train travel in 1 minute?
kilometer(s) per minute

Answers

The answer is 1.5 kilometers per minute

Answer:

1.5

Step-by-step explanation:

In an aquarium, there are 6 large fish and 8 small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.

Answers

Answer:

2/7

Step-by-step explanation:

There are 14 fish and 4 of them are small, red ones.

P(small red fish) = 4/14 = 2/7

hi please help! ill give u a good 5 starz :)

Answers

Answer:

Option C and D!

Step-by-step explanation:

Option C because:-

When 9 is placed in the box after 7, we get:-

7 ÷ 9 = [tex]\frac{7}{9}[/tex] which is correct!

7 ÷ 9 can also be written as [tex]\frac{7}{9}[/tex]. So, this Option is right since the equation is correct when 9 is placed in the box!

Option D is also correct because,

When we place 9 in the box before [tex]\frac{1}{9}[/tex], we get:-

9 ÷ [tex]\frac{1}{9}[/tex] = 81

9 ÷ [tex]\frac{1}{9}[/tex]  equals 9 x 9 (take the reciprocal of [tex]\frac{1}{9}[/tex])

9 x 9 equals 81 which means the equation is correct when 9 is placed in the box!

c and d are the correct answers !

Some1 hurry need help

Answers

Answer:

B) (-6,9)

Step-by-step explanation:

since it's reflecting on the x-axis, the x is gonna stay the same. the y changes though. opposite of -9 is 9.

hope this helps <3

Answer:

B, (-6, 9)

Step-by-step explanation:

this is because it's like as if it was a mirror, so that is the correct answer

the amount of gas used by a household is shown in the table. what is the slope of the data from the table

Answers

Answer. i cant answer this without a pic of the slope

Step-by-step explanation:

There is no picture provided

Sam has a piece of rope that is 3 1/2 feet long he cuts the website that one piece is one 1 1/3

feet long how long is the other piece

Answers

Answer:

2 1/6 ft

Step-by-step explanation:

This problem bothers on subtraction of fraction

Given data

Total length of rope 3 1/2 feet

Let's convert mixed fraction to proper fraction = 7/2ft

First piece of rope = 1 1/3ft

= 4/3ft

Hence the second piece of the rope is = 7/2-4/3= 21-8/6= 13/6

Second piece = 2 1/6 ft

I think

Find the mode 9,10,15,17,15,14,37,45,42,13

Answers

answer:

15

step-by-step explanation:

9, 10, 15, 17, 15, 14, 37, 45, 42, 13

mode means the number that appears the mostin the set of numbers, 15 appears twice, which the others appears only once
The answer is going to be 15

URGENT NEED HELP CLICK TO SEE

Answers

Answer:

3:7

Step-by-step explanation:

15-8=7 green skateboards

3:7

How long will it take the skier to travel 360 meters? Explain how you figured it out.

Answers

20 seconds, I did 72/4=18 then 360/18=20 so a skier travels for 20 seconds and covers 360 meters

Silas just bought a used car for $5000. It loses value at a rate of 30% per year. The value of the car in n years is modeled by the formula f(n)=5000*(0.70)^ n-1 . Approximately how much will the car be worth in 5 years?

Answers

Answer:

$1200.50

plug 5 for n

5000(.7)^4

5000*.2401

=1200.5

Mary has 37 sheep in her flock. If she makes one group of 7 sheep, how many equal groups of 3 sheep can be made with the remaining sheep?

Answers

Answer: 10 groups

Step-by-step explanation:

Since we know she is making a group of 7 sheep, we can do 37-7 to get 30 sheep left

If she wants to find how many groups she can make we have to do 30/3 which gets us to 10 which is the number of groups she can do

I hope this helps

dont give me files. answer on here only.

Answers

Answer:

Look at the image.

Step-by-step explanation:

x
Given the functions f and g in numerical (table ) forms as
-1 0 1 23 4
f(x)
x 1
2 5 5 3 4 3
g(x) 1
Compute: gof (1)
2
0
3
8
4
3
5
2
6
1
Done

Answers

Answer:

[tex]g\ o\ f(1) = 2[/tex]

Step-by-step explanation:

Given

The attached tables

Required

[tex]g\ o\ f(1)[/tex]

This is calculated as:

[tex]g\ o\ f(1) = g(f(1))[/tex]

From the attached tables,

[tex]f(1) = 5[/tex]

So, we have:

[tex]g\ o\ f(1) = g(5)[/tex]

From the attached tables,

[tex]g(5) = 2[/tex]

So, we have:

[tex]g\ o\ f(1) = 2[/tex]

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