Evaluate the limit ....

Evaluate The Limit ....

Answers

Answer 1

It depends on how t is approaching 2.

In fact, if you consider the right limit, you have

[tex] \displaystyle \lim_{t \to 2^+} \dfrac{2-t}{|t-2|} [/tex]

But since t is greater than 2, t-2 is positive, and thus |t-2| = t-2.

So, the limit becomes

[tex] \displaystyle \lim_{t \to 2^+} \dfrac{2-t}{t-2} = \lim_{t \to 2^+} -1 = -1 [/tex]

On the other hand, if you consider the left limit, you have

[tex] \displaystyle \lim_{t \to 2^-} \dfrac{2-t}{|t-2|} [/tex]

But since t is less than 2, t-2 is negative, and thus |t-2| = -t+2.

So, the limit becomes

[tex] \displaystyle \lim_{t \to 2^+} \dfrac{2-t}{-t+2} = \lim_{t \to 2^+} 1 = 1 [/tex]

So, this limit does not exist, because the left and right limits exist but are not the same.


Related Questions

Determine the product of 1,8,5,12

Answers

Hi,

all of them multiplied together is 480.

1x8=8

8x5=40

40x2=80

Answer: 480

Step-by-step explanation:

Since commutative property can be used for multiplication, rewrite it as:

(1 x 8) x (5 x 12)

= 8  x  60

= 480

Solve |2x - 5| = 4. {x | x = -4.5 or x = 4.5} {x | x = 0.5 or x = 4.5} {x | 0.5 < x < 4.5}

Answers

Answer:

{x | x = 0.5 or x = 4.5}

Explanation:

Before we begin, remember that:

The modulus gives the positive value of what's inside it.

This means that:

|a| = |-a| = a

Now, for the given, we have:

|2x-5| = 4

From the above rule, we can deduce that:

either:

2x - 5 = 4

2x = 4 + 5 = 9

x = 4.5 ............> first solution

Or:

2x - 5 = -4

2x = 5-4 = 1

x = 0.5 ..........> second solution

Now, we check:

at x = 4.5: |2(4.5)-5| = |9-5| = |4| = 4 ..........> first solution verified

at x = 0.5: |2(0.5)-5| = |1-5| = |-4| = 4 .........> second solution verified

Hope this helps :)


Answer:

{x | x = 0.5 or x = 4.5}

Step-by-step explanation:

Naya needed to buy boxes of cupcakes for a party.Naya had $60 to spend on the boxes of cupcakes which were each $12.How many boxes can Naya buy for the party?

Answers

5 boxes .. 12 divided by 60

Naya has $60. Each box of cupcakes costs $12.

60÷12=5

Naya can buy 5 boxes of cupcakes.

Change 45/1000 to a equivalent fraction

Answers

Divide both the numerator and denominator by a common multiple.

Divide both by 5 to obtain: 9/200

9/200


Find the GCD (or HCF) of numerator and denominator

GCD of 45 and 1000 is 5

Divide both the numerator and denominator by the GCD

45 ÷ 5

1000 ÷ 5

Consider the system of equations. Which is the Best method to use for solving the system? 4x+y=1 2x+y=8

Answers

4x + y = 1
-2x - y = -8

2x = -7

x = -7/2

2(-7/2) + y = 8

-7 + y = 8

y= 15

elimination

Answer: It is best solve using elimination method

Step-by-step explanation:

4x + y = 1 --------(1)

2x + y = 8---------(2)

subtract (2) from (1)

2x = -7

divide bothside by 2

2x/2 = -7/2

x= -7/2

we can substitute x = -7/2 in any of the equations.

Lets take equation (1)

4x + y = 1

4(-7/2) + y =1

2(-7) + y = 1

-14 + y = 1

y = 1+14

y =15

3.2c + 1.7 = 24.1'

c=

Answers

3.2c+1.7=24.1

First subtract 1.7 from both sides

3.2c=22.4

Now divide both sides by 3.2

c=7

Now put it in the equation.

3.2(7)+1.7=24.1



3.2c + 1.7 = 24.1'

c = (24.1 - 1.7) : 3.2

c = 22.4 : 3.2

c = 7

Which of the following fractions is equivalent to the repeating decimal 0.55555555555...?

A; 5/10

B; 1/2

C; 5/9

D; 55/100

Answers

c. 5/9 ? ? ?

i'm not sure

C.

Any number that is over the denominator 9, will be repeating it self.

which shows the image of quadrilateral ABCD after transformation

Answers

need the image to see the answer

What is the probability of a sum of 3 or 6 or 9?

Answers

100% because
[tex]3 \times 2[/tex]
is 6 and
[tex]3 \times 3[/tex]
is 9 so the sum adds up perfectly

Find the equation of the line that passes through the points (2, 8) and (-2, 6).

(multiple choice)

A. y = -1/2 x + 9

B. y = -2x + 12

C. y = 1/2 x + 7

D. y = 2x + 4

Answers

The correct answer is C. y = 1/2x + 7

In order to find this, we first have to look for the slope. We can do that by using the slope formula below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (8 - 6)/(2 - -2)

m = 2/4

m = 1/2

Now we can solve using the slope intercept form and a given point.

y = mx + b

8 = 1/2(2) + b

8 = 1 + b

7 = b

Now we can put these into the equation and model as y = 1/2x + 7

which rule describes the composition of transformations that maps pre- image ABCD to final image A’’B’’C’’D’’ ?

Answers

In order to identify the transformations from ABCD to A''B''C''D'', carefully analyze changes in position and orientation. If, for instance, you observe a translation to the right by 3 units followed by a clockwise rotation of 90 degrees about point P, the rule in symbolic notation would be: T(3, 0) • R(P, 90)(x, y)

Identify the individual transformations:

Examine the image carefully and determine what transformations are involved in mapping ABCD to A''B''C''D''. Common transformations include translations (shifting), reflections (flipping), and rotations (turning).

Look for clues like changes in position, orientation, or direction to identify the transformations.

Analyze the order of transformations:

Determine the sequence in which the transformations were applied. This is crucial because the order affects the final result.

Look for intermediate images (like A'B'C'D' in your case) that show the effects of individual transformations.

Write the rule in symbolic notation:

Once you've identified the transformations and their order, use appropriate notation to express the composition rule.

Common notations include:

T(a, b) for translation by (a, b) units.

R(O, θ) for rotation about point O by θ degrees.

r(line) for reflection over a line.

Combine the notations for individual transformations using the composition symbol "•" to represent their sequential application.

If you determine that the transformations are a translation by (-6, 1) units followed by a reflection over the x-axis, the rule would be written as:

r(x-axis) • T(-6, 1)(x, y)

Complete question:

Which rule describes the composition of transformations that maps pre- image ABCD to final image A’’B’’C’’D’’ ?

Final answer:

The question seeks a description of the composition of geometric transformations mapping a pre-image to a final image, involving transformations such as translations, rotations, reflections, and dilations.

Explanation:

The question revolves around the concept of geometric transformations, specifically the composition of transformations as they apply to mapping a pre-image (ABCD) to a final image (A''B''C''D''). The composition of transformations includes operations such as translations, rotations, reflections, and dilations. To provide an accurate description of the rule that maps the pre-image to the final image, we would need to know the specific transformations applied in sequence. For instance, if ABCD was translated right by 5 units and then rotated about the origin by 90 degrees, the compositional rule would be a translation followed by a rotation.

What is -35,840-(-14,764)

Answers

21076 is the answer

it's like saying -35840 + 14764

If a and −a are numbers on the number line, which expression MUST give the distance between them?

Answers

Answer:

|2a|

Step-by-step explanation:

Note that distance is positive.  a less -a comes out to +2a, which is the distance between and -a.


Frank and Jack are playing a number game.
Frank tells Jack “I’m thinking of a number between 1 to 10. if I multiply the number by seven and add five I get 26” What number is Frank thinking of?

Answers

3, 7×3=21+5=26, there is your answer

Answer:

It's 3 my G

Step-by-step explanation:

First of all you need to listen to me cause i got you i wouldn't let ya'll down cause i'm trying to get out this dang class

how to write a slope intercept equation from a graph?

Answers

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.


y = -1/2x + 5 is the answer


M = Rise over run meaning you go up 1 and run the other way (left or right) 2

If the measure of angle ABF=6x+26 and the measure of angle EBF=2x9 and measure of angle ABE= 11x-31 find the measure of angle ABF

Answers

Its not clearly given that whether EBF = 2x + 9 or 2x - 9.

I have written the solution for both.

If EBF = 2x + 9,

then ABF = 6x + 26 and ABE = 11x - 31.

Now, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x + 9)

           = (6x + 2x) + (26 + 9)

           = 8x + 35

11x - 8x = 35 + 31

3x = 66

x = 22

Therefore, ABF = 6x + 26 = 6(22) + 26 = 132 + 26 = 158°

If EBF = 2x - 9,

then ABF = 6x + 26 and ABE = 11x - 31.

Now, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x - 9)

           = (6x + 2x) + (26 - 9)

           = 8x + 17

11x - 8x = 17 + 31

3x = 48

x = 16

Therefore, ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°

The expression for angle ABF:  ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°

What is the angle

From the question: If EBF = 2x + 9, then ABF = 6x + 26 and ABE = 11x - 31.

When, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x + 9)

          = (6x + 2x) + (26 + 9)

          = 8x + 35

11x - 8x = 35 + 31

3x = 66

x = 22

Hence, ABF = 6x + 26 = 6(22) + 26 = 132 + 26 = 158°

When EBF = 2x - 9,

So, ABF = 6x + 26 and ABE = 11x - 31.

When, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x - 9)

          = (6x + 2x) + (26 - 9)

          = 8x + 17

11x - 8x = 17 + 31

3x = 48

x = 16

So,  ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°

Learn more about angle  from

https://brainly.com/question/25716982

#SPJ4

word form of 53,200.4

Answers

fifty three thousand two hundred and four

The word form of 53,200.4 would be fifty-three thousand, two hundred and four tenths.

Now remember, to say a number in a decimal in word form, you must remember the names for each placement.

.1 the one would be in the tenths

.01 the one would be in the hundredths; and

.001 the one would be in the thousandths.

I need help

~~~~~
Hggffv

Answers

For a question like this, order of operations must be followed. This can be expressed with PEMDAS.

P arenthesis
E xponents
M ultiplication
D ivision
A ddition
S ubtraction

8^2 ÷ 4 + 3.7(42.3-24.6) -------> Parenthesis first
8^2 ÷ 4 + 3.7(17.7) ------> Now exponents
64 ÷ 4 + 3.7(17.7) ------> Now multiplication and division
16 + 65.49 --------> And finally addition
81.49 which is answer choice C
I hope this helps!

x + 6 = x

with steps please

Answers

Hello!

[tex]x + 6 = x\\[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓

First you had to subtract by the x from both sides of the equation.

[tex]x+6-x=x-x[/tex]

Then refine.

[tex]6=0[/tex]

Answer⇒⇒⇒⇒⇒The sides are not equal.

Answer⇒⇒⇒⇒⇒⇒There are no solution.

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

A gym employee is paid monthly. After working for 3 months,he had earned $4,500. To determine how much money he will make over a six-month period,he created the table below.

Answers

Answer: $9000

A gym employee has earned in 3 months =$4500

Then his monthly salary =$4500/3 =$1500

After six months he will earn = 6 × his monthly salary

= 6×$1500=$9000

His salary table will be as follows

what is a literal equation?
and can it have a pi symbol in it?

Answers

Here are you're answers:

1. A literal equation is a equation where "each of the variables also represent known values." A example of a literal equation is [tex]2300 = 3500 + r[/tex].

2. The answer is "yes." Literal equations can have pi symbols there is a formula that can help solve literal equations. That formula is [tex]V = \frac{\pi}{3} r^2h[/tex].

Hope this helps!

A local hamburger shop sold a combined total of 593 hamburgers and cheeseburgers on Thursday. There were 57 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on thursday

Answers

Answer:

325 hamburgers were sold on Thursday.

Step-by-step explanation:

Let h be the number of hamburgers and c be the number of cheeseburgers.

Using this information we can set up two equation as:

[tex]h+c=593\\c=h-57[/tex]

Now we need to solve these two equations to get the value of number of hamburgers. For that we use substitution method as shown below:

[tex]h+h-57=593\\2h-57=593\\2h=650\\h=325[/tex]

Therefore, the number of hamburgers sold on Thursday were 325.

I solved 4, the answer is 11, seconds: 5x+4(x-3)=87 = x=11, but I don't know how to solve number 5, please anyone explain how to get it!! I'm begging!! GIVING EXTRA POINTS!! BRAINLIST ANSWER!!

Answers

The answer x = 11 is correct for problem 4. Nice work.

Use this x value to find the answer in problem 5. From problem 4, we're told that Romeo runs at a speed of 5 m/s. If he runs for x = 11 seconds,then he runs a total distance of:

5*x =(5 m/s)*(x meters) = (5 m/s)*(11 seconds) = 5*11 = 55 meters

The answer to problem five is 55 meters

Solve the equation. If there is no solution, write no solution. 5|x + 3/4| = 10

Answers

i think the answer is 37/20

I got x=20/37. So there is a solution.

Write an expression that shows how to use the halving and doubling strategy to find 28x50

Answers

Write an expression that shows how to use the halving and doubling strategy to find 28x50

Halving strategy means we divide by 2

Doubling strategy means we multiply by 2

We apply halving strategy for 28 and doubling strategy for 50

Half of 28 is 14

Double of 50 is 100

So 14 * 100 = 1400

Now we check with 28 * 50

28 x 50 = 1400

So required expression is

[tex]\frac{28}{2} * (50*2)[/tex]

1 and 2 please and explain

Answers

I'm sorry I don't know but you can use photomath you can just download it from the App

Anybody need some help

Answers

(A) is correct.


Remember to follow PEMDAS. Parenthesis goes first, or choice (A).


Hope this helps

solve for v in terms of s, t, v. u=-tsv

Answers

the answer will be  is V=8/t


evaluate 4 to the power of 3 . (100/25) - 5 to the power of 0

Answers

Hey there!!

Remember :-

=> Anything to the power 0, is always one.

In the question, is states at the last that the final answer is powered with zero.

Hence, the required answer is "1".

Hope my answer helps!!

Hey there! You could solve this equation by doing PEMDAS [tex]Parentheses[/tex][tex]Exponents[/tex][tex]Multiplication[/tex][tex]Division[/tex][tex]Addition[/tex][tex]Subtraction[/tex][tex]4^3[/tex] [tex](\frac{100}{25})[/tex] [tex]-[/tex] [tex]5^0[/tex][tex]4^3= 64[/tex][tex]64[/tex] [tex]( \frac{100}{25} )[/tex] [tex]-[/tex] [tex]5^0[/tex] [tex]\frac{100}{25}[/tex] [tex]= 4[/tex][tex]64 (4)[/tex] [tex]-[/tex] [tex]5^0[/tex][tex]64(4) =[/tex] [tex]256[/tex][tex]256 -[/tex] [tex]5^0[/tex][tex]5^0 =[/tex] [tex]1[/tex][tex]256 -[/tex][tex]1[/tex] [tex]=255[/tex]Therefore your result (answer) would most likely be: [tex]255[/tex]Good luck on your assignment and enjoy your day! ~[tex]LoveYourselfFirst:)[/tex]

what properties should we use to solve -5 + (5 + 3)?

Answers

im going to say 3 but im not very good at math hope that helps


Other Questions
Which is the ground floor of a building in espaa? Which metal is most likely to be brittle? beryllium iron gold Darwin observed how farmers and breeders produced many kinds of farm animals and plants. These plants and animals had traits that were desired by the farmers and breeders. He also noticed how the study of similar body structures and vestigial organs could add to the evidence of evolution. After performing several breeding experiments, he came to certain conclusions and formulated some theories. His theory of evolution and natural selection is the most accepted one. What is the reason behind the acceptance of Darwin's theory? A)It is supported by practical evidence and examples. B)It is supported by its harmonizing with other views. C)It is based on the ideas of earlier hypothesis and laws. D)It is based on the practical example of Lamarcks theory Emergency medical services differ from regular health care because How many movies did Andrew rent this month if the months bill was $16.25 Which number is prime? 36 37 35 38 Factor. 25x^12-36y^14 The number of question on an exam varies with the number Which words and phrases in the sonnet indicate that the tone is satirical? SELECT TWO options A) my mistressB) Black wiresC) Damaskd D) reeksE) false compare if you place 1 000.00 in a savings account with an interest rate of 3.25%/ month, how much should you earn in interest at the end of the month A- $3.25B-$32.50C-325.00D-$0.33 your client has lived in her modest apartment for several years. The bedroom is small and cluttered. A sewing machine and straight chair are placed in front of the room's only window. She says she sews a lot, usually in the mornings. She has found this room the best place to work because of the morning sun. Which of these is your best approach to this decorating challenge?A: Explain that the room is too cluttered and the sewing machine will have to be kept in a closet and brought out only for use.B: In developing a decorating plan, put the sewing machine into an unobtrusive corner in the large living room and disguise it.C: Refuse the job since there's little hope of success.D: uncluttere the bedroom in other ways. Leave the sewing machine where it isThe answer is D: unclutter the bedroom in other ways. Leave the sewing machine where it is. (PF exam correct) What is 58 - 45.183? A geologist finds a large rock containing a fern fossil. This kind of fern grew on land in hot, moist climates. What does this tell you about the area at the time the rock was formed? A.The area was covered by an ocean. B.The area was snowy and cold. C.The area was hot and tropical. D.The area was muddy and wet. How many grams of a 1000-gram radioactive sample are left after 3 half-lives? *1 point1000 grams500 grams250 grams125 grams2000 grams Write an essay that analyzes the interaction between Christianity, individualism and the growing secularism that began during the Renaissance, and then set it within the story of Henry VIIIs radical break with the Catholic Church and how it changed politics and ecclesiology. Where appropriate, discuss the picture of The Moneylender and his Wife in light of these ideas. If copper (II) sulfate solution and an iron nail are in contact, a replacement reaction occurs. What would the products of the reaction be?2Fe + 3CuSO4 ?2Fe + 3CuSO4Fe2(SO4)3 + 3Cu2Fe + 3Cu + 3S + 3O4 Consider Napoleon's remark that "the story of Rome is the story of the world." What do you think he meant by this? How is it that the "western world grew up in Rome's shadow?" Mrs. Barnett's recipe for zucchini bread calls for 31/2 cups of sugar and 4 eggs. She wants to make 6 batches so hat he has enough for everyone. How much sugar will she need? given that (2,8) is on the graph of f(x),find the corresponding point for the function -3/4 f(x) Which sentence contains a dangling modifier?1) After walking in the blistering sun for two miles, the air-conditioned store felt like paradise.2) Having folded a week's worth of laundry, Heather promised herself she would never wait this long again.3) Exhausted after running the marathon, Antonio collapsed on the couch.4) While feeding the dog, Geri spilled dog food everywhere.