If 2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0, find lim x→2 f(x).

Answers

Answer 1

The value of [tex]\lim _{x \rightarrow 2}[/tex] f(x) by Sandwich theorem is 2.

As per the given data the function limits are:

2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0

Here we have to determine the value of [tex]\lim _{x \rightarrow 2}[/tex] f(x)

Hence by Sandwich theorem:

The sandwich theorem, also known as the squeeze theorem, asserts that if two functions, g (x) and h (x), are squeezed between one another and their respective limits at a given position are both equal to L, then the limit of f (x) at that point is also equal to L.

We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" [tex]\frac{sin(x)}{x}[/tex] between two nicer functions and ​using them to find the limit at x = 0.

[tex]& \lim_{x \rightarrow 2}(2 x-2) \leq\lim_{x \rightarrow 2} f(x) \leq \lim_{x \rightarrow 2}\left(x^2-2 x+2\right) \\[/tex]

[tex]& \Rightarrow 2 \leq \lim _{x \rightarrow 2} f(x) \leq 2 \\[/tex]

Hence [tex]\lim _{x \rightarrow 2}[/tex] f(x) = 2

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Related Questions

58, 72, 74, 92, 84, 40, 74, 81, 76, 83 What was the maximum score earned on Mr. Hill's final exam

Answers

Answer:

92

Step-by-step explanation:

Max= biggest number, surely?

Mrs. Avery is going to randomly select one student from her class to read a poem out loud. There are 15 boys and 13 girls in her class.
What is p (boy)?
If necessary, round your answer to 2 decimal places.

Answers

Answer:

53.57%

Step-by-step explanation:

P(boy) = 15/28 which is 53.57%

Answer:

1.87

Step-by-step explanation:

I found another brainly answer to this question.

How do I solve these problems?

Answers

Answer:

1.) The 1ˢᵗ three term is (-32), (-7) and 18

2.) The 1ˢᵗ three term is 127, 106 and 85

Step-by-step explanation:

1.)

Here,

First Term = a₁ = - 32

Common Difference = (d) = 25

Now, For 1ˢᵗ three term,

n = 1

a₁ = - 32

n = 2

aₙ = a + (n - 1)d

a₂ = (-32) + (2 - 1) × 25

a₂ = (-32) + 1 × 25

a₂ = (-32) + 25

a₂ = -7

n = 3

aₙ = a + (n - 1)d

a₃ = (-32) + (3 - 1) × 25

a₃ = (-32) + 2 × 25

a₃ = (-32) + 50

a₃ = 18

Thus, The 1ˢᵗ three term is (-32), (-7) and 18

2.)

Here,

First Term = a₁ = 127

Common Difference = (d) = -21

Now, For 1ˢᵗ three term,

n = 1

a₁ = 127

n = 2

aₙ = a + (n - 1)d

a₂ = 127 + (2 - 1) × (-21)

a₂ = 127 + 1 × (-21)

a₂ = 127 - 21

a₂ = 106

n = 3

aₙ = a + (n - 1)d

a₃ = 127 + (3 - 1) × (-21)

a₃ = 127 + 2 × (-21)

a₃ = 127 - 42

a₃ = 85

Thus, The 1ˢᵗ three term is 127, 106 and 85

-TheUnknownScientist

A scale drawing of a square has a side length of 8 inches. The drawing has a scale of 1 in. : 6 mi. Find the actual perimeter and area of the square.

Perimeter $=$
mi

Area $=$
mi $^2$

Answers

Answer:

192 mi

2,304 mi²

Step-by-step explanation:

actual side length = 8×6 = 48 mi

so, perimeter of square = 4 × 48 = 192 miles

the area of square = 48×48 = 2,304 sq miles

b. Consider a circle with centre O and radius of 4 units. The distance of point P is 2 units from centre. Find the distance of inverse of point P' from the centre O.​

Answers

The distance of the inverse of point P' from the centre O is also 4 units. This is because the inverse of a point is the point on the opposite side of the circle from the original point, and the radius of the circle is 4 units. Therefore, the distance of the inverse of point P' from the centre O is also 4 units.

What is an unsolvable problem?

Answers

As a result, it may be shown that the answer to the algorithm problem at hand is a halting problem, which is indecidable and thus impossible to solve.

Algorithm : what is it ?

No matter the circumstance, algorithms are fundamentally problem solvers of expression ; they exist to identify, resolve, and frequently automate of solution to a specific problem. Algorithms are frequently introduced in area introductory textbooks by characterizing them as "a series of steps to complete a problem."

Here,

one of the most common problems that hasn't been solved is the stopping problem. It asks the following question:

Does M come to a standstill when given the input w for any Turing machine with the parameters alphabet = a, b, and any string w over

It can be shown that the halting problem cannot be resolved since it is indecisive.

As a result, it may be shown that the answer to the algorithmic problem at hand is a halting problem, which is indecidable and thus impossible to solve.

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Write 1 and 3/8 as an improper fraction.

Answers

1 3/8 as an improper fraction is 11/8

Answer:

1 3/8 = 11/8 as a improper answer

Step-by-step explanation:

You have to make your whole number into a numerator along with your original numerator.

Improper fraction: When your numerator is greater than your denominator.

What should be added to 7x^2 5x 1 to get 3x^2 4x 7?

Answers

The value should be added will be [tex]y = -4x^{2} +9x+6[/tex]

Now, According to the question:

Let the value y be added to  [tex]7x^2-5x+1[/tex] to give [tex]3x^2+4x+7[/tex]

y =  [tex]3x^2+4x+7[/tex] - ( [tex]7x^2-5x+1[/tex])

y = [tex]3x^{2} +4x+7-7x^{2} +5x-1[/tex]

Combine like terms:

y = [tex]3x^{2} -7x^{2} +4x+5x+7-1[/tex]

Calculate the subtraction and addition.

[tex]y = -4x^{2} +9x+6[/tex]

Hence, The value should be added will be [tex]y = -4x^{2} +9x+6[/tex].

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The complete question is this:

What should be added to  [tex]7x^2-5x+1[/tex] to get [tex]3x^2+4x+7[/tex] ?

Pls help me I’ll give thxs and brainiest if you answer correctly to both exercises

Answers

Answer:

Activity 1

1. a.8, b.4, c.8, d.12

2. a.10, b.8, c.20, d.40

3. a.16, b.9, c.40, d.27

Activity 2

1. a.10, b.40, c.15

2. a.4, b.35, c.14

3. a.80, b.20, c.2.5

I'm going to try this one more time...

Which of these characteristics of a star make it most likely to become a black hole? Select the TWO!!!! correct answers.

A. Its mass is equal to that of the sun.

B. It has an abundant supply of hydrogen.

C. Its mass is greater than 20 times the mass of the sun.

D. It is dying.

Answers

Answer and Step-by-step explanation:

C and D  is the answer.

It needs a lot of mass so that it can collapse on itself to form a black hole, and when it dies, it also collapses on itself, forming a black hole.

A is incorrect because the mass of our sun hasn't made it to collapse, and it still has some billions of years before the mass increases.

B is incorrect because the hydrogen needs to be depleted in order for the sun/star to start the nuclear process.

#teamtrees #PAW (Plant And Water)

Pythagorean Theorem & irrational Numbers Question
Which of the following could not be the lengths of sides of a
right triangle?
Select one:

8, 10, 12

6, 8, 10

9, 12, 15

8, 15, 17

Answers

Answer:

2nd

Step-by-step explanation:

Gerry is reading a book that has 475 pages. He already read some of it last week. He plans to read 160 pages tomorrow. By then, he will be 4/5 of the way through the book. How many pages did Gerry read last week? Which equation bests represents the situation?

w + 160 = (4/5) 475
w + 20 = (2/3) 276
475 = 160 - (4/5) b

Answers

475=160-(4/5)b is the correct answer

150 people went to see "Ode to Algebra" performed in the school auditorium. If the number of children that attended the performance was c, how many adults attended?​

Answers

Answer:

150-c

Step-by-step explanation:

150= total

c= children

adults=x

x=150-c

Can you let me know the answer please

Answers

Answer:

The answer is A

Step-by-step explanation:

When looking at this image, look at A, notice how it says y and the equal to symbol is facing it? then notice at the end of answer a is -4, look at the graph and the line intercepts -4, remeber, the end number, whether positive or negative will always be the on the y axis

Select the correct volume.
A brick has a base area of
of 384
square inches and a height of 22 inches. What is the volume of the brick?
40
3
cubic inches
4.
15
cubic inches
10
5
95 cubic inches
8
1
239
Cubic inches
16

Answers

Answer:

the answer is 10 5. you welcome

Please answer the question in the picture and show your work! I got tan= square root of 2 but I’m not sure if that’s right and if there’s more answers since it wants all values of tan. This is due tomorrow please help!

Answers

Answer:

tan(θ) is undefined.

Step-by-step explanation:

Recall that tan(θ) = sin(θ) / cos(θ). We are given that sin(θ) = -1. Hence:

[tex]\displaystyle \tan\theta=\frac{\sin\theta}{\cos\theta}=-\frac{1}{\cos\theta}[/tex]

Since 1 / cos(θ) = sec(θ):

[tex]\tan\theta=-\sec\theta[/tex]

We can square both sides:

[tex]\tan^2\theta=\sec^2\theta[/tex]

From the Pythagorean Identity:

[tex]\tan^2\theta+1=\sec^2\theta[/tex]

Substitute:

[tex]\tan^2\theta+1=\tan^2\theta[/tex]

So:

[tex]1\neq0[/tex]

Since we acquire an untrue statement, no solutions exist.

If needed, refer to the unit circle. Recall that sin(θ) only equals -1 when θ = 3π/2 (on the interval [0, 2π)). At 3π/2, cos(θ) = 0. Since tan(θ) = sin(θ) / cos(θ), tan(θ) is undefined whenever sin(θ) = -1 (or 1).

A bakery sells chocolate cupcakes and vanilla cupcakes. It sold 400 cupcakes in a day,
and 17% of them were vanilla. How many of the cupcakes sold that day were
chocolate?

Answers

Answer:

332 chocolate cupcakes.

Step-by-step explanation:

17% of 400 = 68

400 - 68 = 332

I am giving away 10 points to anybody who provides correct answers with explanations.

Answers

Answer:

[tex]5)\ f(n) = 4v[/tex]

[tex]6)\ \frac{1}{4}n[/tex]

[tex]7)\ True[/tex]

This might not be correct though. I'm only in middle school lol. I am sure about the last one.

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answers

Answer:

u can download the gauthmath app it's very helpful i PROMISE :)

Answer: Answer: −9±√−255/ 24

Step-by-step explanation:

12a2+9a+7=0

a=12, b=9, c=7

12a^2+9a+7=0

a=12, b=9, c=7.

−b±√b2−4ac/ 2a

−(9)±√(9)2−4(12)(7)/ 2(12)

Mhanifa please help! This is due soon

Answers

Answer:

1) x²=256-64

x=8√3

2). x²=200+81

x=√281

3). x²=169+36

x=√205

3).

Step-by-step explanation:

here's your solution

==> in figure 1,

= perpendicular^2 = hypotenuse^2 - base^2

= x^2 = 16^2 - 8^2

= x^2 = 256 - 64

= x^2 = 192

= x = √192

= x = 13.85

==> in figure 2,

= hypotenuse^2 = Perpendicular^2 + base^2

= x^2 = 40^2 + 9^2

= x^2 = 1600 + 81

= x^2 = 1681

= x = √1681

= x = 41

==> in figure 3,

= hypotenuse^2 = Perpendicular^2 + base^2

= x^2 = 13^2 + 6^2

= x^2 = 169 + 36

= x^2 = 205

= x = √205

= x = 14.31

[tex]hope \: it \: helps.....[/tex]

Help.....ASP Please help right now

Answers

The triangle with side lengths given in the question can be classified as a scalene triangle.

What is a scalene triangle?

A scalene triangle is a type of triangle in which none of its three given length of sides are equal. It can be differentiated from other types with respect to  this property.

A triangle is a plane shape which can be described by three sides and three measure of internal angles. Some other types of triangle are: equilateral, obtuse, isosceles etc. The sum of all internal angles of a triangle is 180^o

Considering the given length of sides in the question, it can be proven the the only type of triangle that can be formed is a scalene triangle. Therefore, the triangle can be classified as a scalene triangle.

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In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?

Answers

The population of the city grew from 2010 to 2020 by 13.37 %

What is percentage?

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

The population in 2015 =

A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

The population in 2015 =

A = 237,000(1+0.076)⁵

A = 341829.629

The population in 2020 =

A = P (1-r)ⁿ

A = 341829.629(1-0.047)⁵

A = 268704.047

Percent grow = 268704.047 - 237,000 / 237,000 × 100

= 31704.047 / 237,000 × 100

= 13.37 %

Hence, the population of the city grew from 2010 to 2020 by 13.37 %

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( 1/2 ) ^2
HELP!
ME!

Answers

Answer:

1/4 is the answer

just multiply 1/2 x 1/2

hope this helps

have a good day :)

Step-by-step explanation:

1/2 x 1/2 =1/4 ^2 to just multiply the inside by itself twice.

97 = 10x + 27 need help!!

Answers

Answer:

x=7

Step-by-step explanation:

97 = 10x + 27

97 - 27 = 10x

70 = 10x

70/10 = x

7=x

Answer:

X=7

HOPE THIS HELPS

-Todo ❤️

Step-by-step explanation:

97=10x+27

-27. -27

70=10x

/10. /10

X=7

Carl wants to find the product 30×56.
Which of the following best explains how he can find the product mentally?
A.


He knows that 30÷5 is 6. He then multiplies 6 by 6 to get 36.
B.


He knows that 30×66is 30. He then subtracts 1 from 30 to get 29.
C.


He knows that 3×6=18. He then adds 18 and 5 to get 23.
D.


He knows that 30×16is 5. He then multiplies 5 by 5 to get 25.

Answers

Answer:

Your answer will be D. He knows that 30 × 16 is 5 then multiples 5 by 5 to get 25.

PLS WHAT IS THE VALUE OF X SOMEONE

Answers

Answer:

It would be 166 degrees.

Step-by-step explanation:

Do 180-97 to get 83 degrees

Since the triangle is a isosceles triangle, the opposite side of it would also be 83 degrees, so 83+83

With this, do 180-83-83 to get 14 degrees for the third interior angle

Last, subtract this from 180 to get the value of x, 166 degrees.

Hope that helps.

Show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1
On the interval
(−[infinity], 1),
f is function; therefore f is continuous on
(−[infinity], 1).
On the interval
(1, [infinity]),
f is function; therefore f is continuous on
(1, [infinity]).

Answers

The function [tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]  is continuous on (-∞, ∞).

As per the given data the function f(x) is given by:

[tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]

Here we have to determine that the function f(x) is continuous on (-∞, ∞)

If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)

What are continuous function?

A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.

To show f(x) is continuous at x = 1

[tex]\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}[/tex] f(x)

[tex]\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\[/tex]

= 1 - 1

= 0

[tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\[/tex]

= ln 1

= 0

Therefore  [tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0[/tex].

Hence f(x) is continuous on (-∞, ∞)

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I’ll give brainliest

Answers

Answer:

Step-by-step explanation:

P of red or green = (40 red+ 10 green)/ (40 red +50 yellow+10 green)

= 50/ 100= 1/2

PLEASE HELP NOW THANK YOU<3

Answers

Answer:

sheeeeeeeeeesh

Step-by-step explanation:

Answer:

y = -4/5x +1

Step-by-step explanation:

Slope formula says that y=mx+b.

In terms of words, it means that y is equivalent to slope times x plus the y-intercept.

Slope= rise/run. You rise 4 and run 5. (which is 4/5) However, the slope is negative so be careful with that.

We know the y intercept is 1 so replace that for b.

Put it together and you get y=-4/5x+1

hope this helps!!

What are the 3 types of trigonometry?

Answers

the main three types of trigonometry are ,

1- sine angle (sin Q)

2- cosine angle (cos Q)

3- tangent angle (tan Q)

all the other types of trigonometry are related to these three types only.

sine angle

we can find out the sine angle by taking perpendicular of the triangle divided by hypotenuse of the triangle. sine angle is a acute angle.

cosine angle

we can find out the cosine angle by taking base of the triangle divided by hypotenuse of the triangle. cosine angle is a acute angle.

tangent angle

we can find out the sine angle by taking perpendicular of the triangle divided by base of the triangle.

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