Prove that limx→2 2^x=4 using the formal definition of limit​.​

Answers

Answer 1

Answer:

Refer to step-by-step

Step-by-step explanation:

Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]

Plug in the value of 2 into the limit.

[tex](2)^{2}=4[/tex]

Thus we proved the limit.


Related Questions

Lillian is wrapping a gift box that has the size shown below. What is the volume of the box?
Enter your answer in the box.

Cube with height of 9 cm and area of base as 36 square cm.

cubic centimeters

Answers

[tex] \huge \mathrm{Answer࿐ }[/tex]

[tex] \boxed{\mathrm{volume = area \times height}}[/tex]

[tex]36 \times 9[/tex]

[tex]\mathrm{324 \: cm {}^{3} }[/tex]

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

Answer:

324

Step-by-step explanation:

if you do 36 times 9 you get 324

PLS BELP I DONT HAVE MUCH TIME!!!

Answers

Answer:

I'd say A or D but I have a feeling it's A

Zachary purchased a computer for $1,800 on a payment plan. Three months after he purchased the computer, his balance was 1,350. Five months after he purchased the computer , his balance was 1,050. What is an equation that models the balance B after m Months

Answers

Answer: y = -150x + 1800

Step-by-step explanation:

1. Find the linear slope of the line between two points.

(Change in Y)/(Change in X)

2. Write out an equation in point slope form.

(y-y1) = m(x-x1)

y-1800 = -150(x-0)

3. Simplify the equation and turn it into slope-intercept form.

y = -150x + 1800

Can y’all help me on question 13?!

Answers

Answer:

C

Step-by-step explanation:

20 - 13 = 7

Answer:

C)

Step-by-step explanation:

7 + 13 = 20

The answer is C

Using pi 3 what is the answer

Answers

Answer:

12mm

Step-by-step explanation:

circumference (distance around) is equal to πd.

here, if π is 3, we do 3 x the diameter, which is 4. 3 x 4 = 12mm

Select the correct answer.
Which statement is true about function f, which is shown in the graph?
f(x) = -805 + 413 + 5x

Answers

Answer:

The function is neither even nor odd.

Step-by-step explanation:

A function is odd if:

f(x) = - (f-x)

A function is even if:

f(x) = f(-x)

A function is neither odd nor even if neither of the above two equalities are true, that is to say:

f(x) != f(-x) and f(x) != -f(-x)

Which is our case. (because substituting (-x) in place of (x) will not give us either of the equations. So the function is neither odd, nor even.

A bakery made 100 donuts, in the display case, 40/100 were chocolate, 3/10 were glazed and cinnamon. which fraction of the donuts were cinnamon?​

Answers

57 of them were cinnamon.

Explanation:

100-40 = 60 and 3 of those were glazed so that leaves us with 57

Answer:

57/100

Step-by-step explanation:

Consider the set {1, 2, 3, 4}.

a. Make a list of all samples of size 2 that can be drawn from this set of integers.
b. Construct the sampling distribution of sample means for samples of size 2 selected from this set.
c. Provide the distribution both in the form of a table and histogram.

Answers

Answer:

(a)

[tex]List = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),\\(4,1),(4,2),(4,3).(4,4)\}[/tex]

(b) Sampling Distribution (Table)

[tex]\begin{array}{cccccccc}{\bar x} & {1} & {1.5} & {2} & {2.5} & {3} & {3.5} & {4} & {Pr}& {\frac{1}{16}} & {\frac{1}{8}} & {\frac{3}{16}} & {\frac{1}{4}} & {\frac{3}{16}} & {\frac{1}{8}} & {\frac{1}{16}} \ \end{array}[/tex]

(b) Sampling Distribution (Histogram)

See attachment

Step-by-step explanation:

Given

[tex]Set = \{1,2,3,4\}[/tex]

[tex]n =4[/tex]

Solving (a): A list of sample size 2

We have:

[tex]n =4[/tex]

[tex]r = 2[/tex] --- the sample size

First, we calculate the number of list using permutation (orders matter)

[tex]n(List) = n^r[/tex]

So, we have:

[tex]n(List) = 4^2[/tex]

[tex]n(List) = 16[/tex]

And the list is:

[tex]List = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),\\(4,1),(4,2),(4,3).(4,4)\}[/tex]

Solving (b): Sample distribution  of sample means of (a)

First, calculate the mean of each set using:

[tex]Mean = \frac{Sum}{2}[/tex]

So, we have:

[tex](1,1) \to \frac{1+1}{2} \to 1[/tex]       [tex](1,2) \to \frac{1+2}{2} \to 1.5[/tex]    [tex](1,3) \to \frac{1+3}{2} \to 2[/tex]    [tex](1,4) \to \frac{1+4}{2} \to 2.5[/tex]

[tex](2,1) \to \frac{2+1}{2} \to 1.5[/tex]    [tex](2,2) \to \frac{2+2}{2} \to 2[/tex]     [tex](2,3) \to \frac{2+3}{2} \to 2.5[/tex]    [tex](2,4) \to \frac{2+4}{2} \to 3[/tex]

[tex](3,1) \to \frac{3+1}{2} \to 2[/tex]       [tex](3,2) \to \frac{3+2}{2} \to 2.5[/tex]    [tex](3,3) \to \frac{3+3}{2} \to 3[/tex]    [tex](3,4) \to \frac{3+4}{2} \to 3.5[/tex]

[tex](4,1) \to \frac{4+1}{2} \to 2.5[/tex]    [tex](4,2) \to \frac{4+2}{2} \to 3[/tex]    [tex](4,3) \to \frac{4+3}{2} \to 3.5[/tex]    [tex](4,4) \to \frac{4+4}{2} \to 4[/tex]

Write out the sample means (sorted)

[tex]\bar x =\{1,1.5,1.5,2,2,2,2.5,2.5,2.5,2.5,3,3,3,3.5,3.5,4\}[/tex]

Construct a frequency table

[tex]\begin{array}{cc}{\bar x} & {f} & {1} & {1} & {1.5} & {2} & {2} & {3} & {2.5} & {4} & {3} & {3} & {3.5} &{2} & {4} & {1} & Total & 16\ \end{array}[/tex]

Construct the sampling distribution where the probability is calculated using: [tex]\frac{f}{Total}[/tex]

So, we have:

[tex]\begin{array}{cccccccc}{\bar x} & {1} & {1.5} & {2} & {2.5} & {3} & {3.5} & {4} & {Pr}& {\frac{1}{16}} & {\frac{1}{8}} & {\frac{3}{16}} & {\frac{1}{4}} & {\frac{3}{16}} & {\frac{1}{8}} & {\frac{1}{16}} \ \end{array}[/tex]

A national survey asked 1,501 randomly selected employed adults how many hours they work per week. Based on the collected data, a 95 percent confidence interval for the mean number of hours worked per week for all employed adults was given as (41.18, 42.63). Which of the following statements is a correct interpretation of the interval?
A. Ninety-five percent of all employed adults work between 41.18 hours and 42.63 hours per week.
B. The probability is 0.95 that a sample of size 1,501 will produce a mean between 41.18 hours and 42.63 hours.
C. Of all samples of size 1,501 taken from the population, 95% of the samples will have a mean between 41.18 hours and 42.63 hours.
D. We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.
E We are 95% confident that the mean number of hours worked per week for all employed adults is between 41.18 hours and 42.63 hours.

Answers

Answer:

C

Step-by-step explanation:

The correct statement about the interpretation of the interval is

We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.

Option D is the correct answer.

What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown parameter, such as a population means or proportion, based on a sample of data from that population.

It is a statistical measure of the degree of uncertainty or precision associated with a statistical estimate.

We have,

We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.

This is the correct interpretation of the 95% confidence interval given for the mean number of hours worked per week for all employed adults, based on the data collected from the random sample of 1,501 employed adults.

It means that if we were to take many random samples of 1,501 employed adults from the population and calculate the mean number of hours worked per week for each sample, we can be 95% confident that the true population mean lies between 41.18 hours and 42.63 hours.

Thus,

The correct statement about the interpretation of the interval is

We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.

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△ABC ~ △DEF What is the scale factor between them?

Answers

2/3

6x = 4
x = 2/3

The scale factor can be determined by using similar sides


Someone please help me. I will give you hella points I need this answer to like graduate type

Answers

Answer:

$9 and $7

Step-by-step explanation:

The first equation:

x + 2y = 23

The second equation:

2x + 3y = 39

Convert to slope-intercept form:

x + 2y = 23 ⇒ 2y = -x + 23 ⇒ y = -1/2x + 11.52x + 3y = 39 ⇒ 3y = -2x + 39 ⇒ y = -2/3x + 13

The graph is attached

Intersection point is (9, 7)

Adult tickets cost $9Child tickets cost $7

simply the following​

Answers

Answer:

n

Step-by-step explanation:

[tex]\Bigg[\bigg[ [1/n]^{-1}\bigg]^{-1} \Bigg] ^{-1}[/tex]

=[tex]\bigg[ [1/n]^{-1}\bigg]^{(-1) (-1)}[/tex]

=[tex]\bigg[ [1/n]^{-1}\bigg]^{1}[/tex]

=[tex] [1/n]^{-1\times 1}[/tex]

=[tex] [1/n]^{-1}[/tex]

=[tex] [1/n^{-1}][/tex]

= n

Hope it helps you in your learning process

Please help. the answer is not b

Answers

Answer:

I believe its C. If not then it is A. :D

Step-by-step explanation:

How many edges does the figure have?
3
O
5
6
O O
01

Answers

I think the answer is 9 , maybe 6

Answer:

It is.... 9! i got it right on edgunity 2022! sorry plase exscuse my spelling! Step-by-step explanation:

#la:What is the axis of symmetry?*
#16: What is the vertex? *

Answers

Answer:

Vertex: (-1,-4)

Axis of Symmetry: x=-1

Step-by-step explanation:

The vertex is the minimum of the parabola, or (h,k), which is located at (-1,-4)

The axis of symmetry is a vertical line that marks the halfway point of the parabola, which is equal to x=h. Therefore, the axis of symmetry is x=-1

please help me with this thank you.​

Answers

A) 4:00 PM
B) 1:55 PM

The shaded numbers show a pattern in the multiplication table. Which
expression can find the number that comes next in the pattern?
5
X 0 1 2 3 4
0 0 0 0 0 0
1 0 1 23 4
0
5
0
2.
46
8
10
AWN
O
3
12 15
0
4
Lololo
12 16 20
5
0
5
10 15 20 25
25 + 11
25 x 6
25 X 4
25 + 1

Answers

25+1=26 25x4=100 this is the answer

If Jorgen has $4,000,000,000,000 And he wants to buy a truck123456789,-0000000000000000000000000000000000000,00000000000000000000000,00000000000000000000 haw much will he need to save up to buy the truck?

Answers

He doesn't need a truck. He can buy an aeroplane.

Answer:

Jorgen would still have enough money for the truck.

Step-by-step explanation:

Seeing as - (or negative) 0000000000000... isn't a real number and you put a comma after the 123456789, Jorgen would actually have enough for the truck. If you actually wanted the truck to be worth 123456789000000000... Jorgen would need to save up more than 9 octovigintillion to reach his goal of getting the truck, and that is one expensive truck.

Given f(x) and g(x) are polynomials, is the product always a polynomial? Justify your argument.



The product of f(x) and g(x) is , .
select choice(sometimes never always)
a polynomial. By the definition of polynomials the product of polynomials is ,
Select Choice(sometimes never always)
a polynomial because the ,
Select Choice(exponents coefficients variables)
are real numbers and the ,
Select Choice(exponents coefficients variables)
are whole numbers. Real numbers and whole numbers are ,
Select Choice(closed not closed
under addition and subtraction.

Answers

The complete statement about the product of the polynomials is that:

The product of f(x) and g(x) is always a polynomial because the coefficients are real numbers and the exponents are whole numbers. Real numbers and whole numbers are closed under addition

How to complete the statements

From the question, we have the following parameters that can be used in our computation:

Polynomials f(x) and g(x)

When these polynomials are multiplied;

We get another polynomial

This is because, when you multiply two polynomials you get a sum of monomials.

A sum of monomials is always a polynomial

The sum of monomials stated above implies that the whole exponents and the real coefficients are closed under addition

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Which equation justifies why ten to the one third power equals the cube root of ten?

ten to the one third power all raised to the third power equals ten to the one third plus three power equals ten

ten to the one third power all raised to the third power equals ten to the one third times three power equals ten

ten to the one third power all raised to the third power equals ten to the three minus one third power equals ten

ten to the one third power all raised to the third power equals ten to the one third minus three power equals ten

Answers

The equation that justifies  ten to the one third power equals the cube root of ten is ten to the one third power all raised to the third power equals ten to the one third times three power equals ten. Option B

How to justify the power

we are to find [tex]10^{\frac{1}{3} } = \sqrt[3]{10}[/tex]

The justification has to be done with the use of the properties of powers as well as roots.

[tex]a^\frac{m}{n} = \sqrt[n]{a^m}[/tex]

then we would have:

[tex]\sqrt[3]{10} = \sqrt[3]{10^1} =10^\frac{1}{3}[/tex]

then we would have

[tex](10^\frac{1}{3} )^3\\\\= 10^\frac{3}{3}[/tex]

= 10

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Cali made a drawing for her parents for a gift. She wanted to frame it. Her drawing has an area of 96 cm and a width of 8 cm. How many cm of the wooden frame will she need?

Answers

Answer: 40 cm

Step-by-step explanation:

The wooden frame needed = perimeter of the drawing
The length of the picture: 96 :8 = 12cm
The perimeter: (12 + 8) x 2 = 40 cm

Single payment loan for $1200 repay in 120days interest rate is 7%, what is the maturity value of the loan?

Answers

The maturity value of the loan based on the calculation is $1227.72

How to illustrate the interest?

From the information, single payment loan for $1200 repay in 120days interest rate is 7% and we want to calculate the maturity value of the loan.

It should be noted that the interest will be calculated as:

= Principal × Rate × Time

= 1200 × 7% × (120/360)

= 1200 × 0.07 × 0.33

= $27.72

Maturity amount = $1200 + $27.72

Maturity amount = $1227.72.

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Question 5, Please Answer and Explain

Answers

The trigonometric ratios for the angle x in the triangle are given as follows:

tan(x) = f/e.cos(x) = e/d.sin(x) = f/d.

What are the trigonometric ratios?

The three trigonometric ratios are defined as follows:

Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.

In the right triangle in this problem, we have that d represents the hypotenuse, while the sides relative to angle x are given as follows:

Adjacent side: length of e.Opposite side: length of f.

These sides are used along with the definitions of each ratio to give the three trigonometric ratios of angle x.

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What is the value of P for the following triangular prism? 19 yd 12 yd 6 yd 18 yd

Answers

Answer:

12 yds

Step-by-step explanation:

I just answered it. :)))

Answer:

option C

Step-by-step explanation:

The answer is 12 yd. All you muxt do is find the volume.

or one batch of cookies, Sabrina needs 2 cups of flour. Sabrina is going to make 1, batches of cookies. How much flour will she need? A. О 1 cups B.O 2 cups C. 3 cups D. 3 cups​

Answers

Answer:

B

Step-by-step explanation:

They basically give the answer.

Answer:

I am a bit confused. You stated that "Sabrina is going to make 1, batches of cookies" and you also wrote "for one batch of cookies, Sabrina needs 2 cups of flour." Hence, your answer should be 2 cups like you previously stated. However, I think that the question is wrong.

Step-by-step explanation:

find the truth value Of 3+4= 12, then 3+2=6​

Answers

The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.

What is Truth Values?

Truth value is defined as whether the given proposition is either true or false, not both.

Here the proposition is of the form if p, then q.

Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.

Here, both of the propositions are false.

The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.

Here, since both of the statements are false, the truth value is true.

Hence the truth value of the given proposition is true.

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d= c/n solve for n, I've been trying to solve this by multiplying by n but i want to solve for n so that's wrong thank you guys :D

Answers

Answer:

You started correctly....

Step-by-step explanation:

d = c/n      Multiply both sides by 'n'

dn = c        now divide both sides of the equation by 'd'

n = c/d       Done.

Determine the greatest common factor of the following numbers 8 and 12
NO LINKS PLEASE!!!!​

Answers

I think it would be 4.
8 breaks down to 4(2) and 12 breaks down to 4(3). Let me know if that helps!

Plz help me well mark brainliest if correct!!

Answers

Answer:

1 hour

Step-by-step explanation:

Each graph shown lasts for 1/2 hour / 30 minutes

I need help ASAP...please please someone help

Answers

Answer:

x = 26

Step-by-step explanation:

180=(4x+10)+(x+40)

180 = 4x + x +10 + 40

180 - 50 = 5x

130 = 5x

130 / 5 = x

26 = x

A 130+50.
Hdhdhdbsnna
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