Determine whether the function is continuous on the entire real number line. Explain your reasoning.

Determine Whether The Function Is Continuous On The Entire Real Number Line. Explain Your Reasoning.

Answers

Answer 1

So,

Given the function:

\(f(x)=\frac{4}{x^2-36}\)

To check if the function is continuous in the entire number real line, we need to analyze the restrictions in the domain.

As you can notice, the denominator of a rational function can't be zero, so:

\(x^2-36\ne0\)

We're going to find the values of x such that:

\(x^2-36=0\)

This is:

\(\begin{gathered} x^2=36 \\ x=\pm6 \end{gathered}\)

As you can see, "x" can't take the values of 6 and -6. If that happens, the function is not defined. Thus, the function is not continuous on the entire real number line.


Related Questions

Anthony owns a bakery and buys raw eggs in packs of 50 for $5.00 each. The delivery is a set free of $10.00. If Anthony has $100.00 to spend, what is the domain of this function, where x represents the number of packs of eggs?

Answers

Answer:

D- The set of whole numbers were 1<_x<18

Step-by-step explanation:

Which expression is equival 81 1/3?

Answers

Answer: 3^3 Square root 3

Step-by-step explanation:

Show three ways you can represent three eighths

Answers

HERE IS THE ANSWER!!

Show three ways you can represent three eighths

Given the expression √x can x be a negative number? Why or why not?

Answers

No, because the square root of a negative number is called an imaginary number.

What is the area of the triangle?
Vx
5 in
3 in.
4 in
O 6 square inches
ola
square inches
O 10 square inches
O 12 square inches

What is the area of the triangle?Vx5 in3 in.4 inO 6 square inchesolasquare inchesO 10 square inchesO

Answers

The answer is 6 square inches

Sera had the number 548.She adds one to the tens and two to the units. What number would Sera end up with??​

Answers

The number she'd have is:

560

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

Hence, Sera ends up with 560.

Can someone help me with this problem?

Can someone help me with this problem?

Answers

Answer:

Lin

Step-by-step explanation:

5/7*2/2=10/14

3/2*7/7=21/14

10/14+21/14=31/14

Answer:

Lin

Step-by-step explanation:

You should give the other person brainliest

What is cos(tan^-1(-2/3))=

Answers

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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Give an example of each of the following, or argue that such a request is impossible.

a. A sequence that has a subsequence that is bounded but contains no subsequence that converges.
b. A sequence that does not contain 0 or 1 as a term but contains subsequences converging to each of these values.
c. A sequence that contains subsequences converging to every point in the infinite set {1, 1/2, 1/3, 1/4, 1/5,...}.
d. A sequence that contains subsequences converging to every point in the infinite set {1, 1/2, 1/3, 1/4, 1/5,...}, and no subsequences converging to points outside of this set.

Answers

Answer and Step-by-step explanation:

Solution:

(a) Let (bn) be a bounded sequence of (an) then, Bolzano- Weierstrass theorem,

(bn) contains a subsequence that is converges.

(b) The sequence :

Xn = 1 + (-1) n / 2 + 1/n

Clearly, (xn) does not contain 1 or 0.

If we take sequence (x2n), then it converges to 1 and when we take sequence (x2n+1),

Then it converges to 0.

(c) The sequence:

1

1,1/2

1, 1/2, 1/3

1, 1/2, 1/3, 1/4

i.e

(xn) = (1,1/2, 1, 1/2, 1/3, …)

Then, the subsequence (xn) that is identically ½ in second column and 1/3 is third column and so on.

It has sub sequence that converges to every point in infinite set {1, 1/2, 1/3, 1/4, 1/5…}.

(d) The sequence

{1, 1/2, 1/3, 1/4, 1/5…}

if we take sequence of given set, then, this set converges to zero. This is not contained in it.

If (xn) converges to every point in set {1, 1/2, 1/3 …} then there exists subsequence which converges to 0. And 0 does not belong to given set.

is the graph discrete or continuous I really need help

is the graph discrete or continuous I really need help

Answers

The graph is continuous

The graph has points that are not scattered, so it is continuous.

A restaurant hands out a scratch-off game ticket with prizes being worth purchases at the restaurant. The back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100. What are the odds that the ticket is worth at least $25?

Answers

Answer: 0.05412

Step-by-step explanation:

Formula : Odds of having an event is given by  \(o=\dfrac{p}{1-p}\), where p = probability that event happens.

In terms to find p , we use \(p=\dfrac{o}{1+o}\)

Given, he back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100.

Let X be the worth of ticket.

Then, the probability that the ticket is worth at least $25 =

\(P(X\geq 25)=P(X=25)+P(X=50)+P(X=100)\)

\(=\dfrac{0.04}{1+0.04}+\dfrac{0.01}{1+0.01}+\dfrac{0.003}{1+0.003}\\\\=0.05135\)

The odds that the ticket is worth at least $25 = \(\dfrac{0.05135}{1-0.05135}\)

=0.05412

hence, the odds that the ticket is worth at least $25 is 0.05412 .

10 times as many as 1 ten is ________ tens

Answers

Answer:

100

Step-by-step explanation:

1 ten = 10

Soo...10 ×10= 100

I need help with find the length of side AC\(can \: u \: help \: me \: on \: us\)

I need help with find the length of side AC[tex]can \: u \: help \: me \: on \: us[/tex]

Answers

\(AC\text{ = 16}\)

When two triangles are similar, the ratio of their corresponding sides are equal

Thus, we have it that;

\(\begin{gathered} \frac{AB}{AC}\text{ = }\frac{PQ}{PR} \\ \frac{20}{AC}\text{ = }\frac{50}{40} \\ \\ AC\text{ = }\frac{40\times20}{50}\text{ = 16} \end{gathered}\)

CAN SOMEONE PLZ ANSWER THIS ITS DUE AT 11:59 APRIL 11 2021 AND ILL MARK U BRAINLIST

CAN SOMEONE PLZ ANSWER THIS ITS DUE AT 11:59 APRIL 11 2021 AND ILL MARK U BRAINLIST

Answers

Answer:

answer is c

Step-by-step explanation:

Answer:

c. 586.2

Step-by-step explanation:

add all areas together:

127.2 for semi circle on right

22x18=396 for middle square

7*9=36 for 2 triangles on left

Which ratio is equivalent to the ratio 2.5

Answers

2:5 = 4:10 i think
sorry if this is wrong!:(

Round 9.948 to the nearest whole number.

Answers

Answer: 9.900

i had this before the answer is right.

A 1 liter bottle of Mexican wine costs 100 pesos. At that price, how much would a
gallon jug of wine cost in US dollars? Round to two decimal places. SHOW ALL
WORK. (In other words, what is the price in dollars per gallon.)

Answers

It is 4.86$ in U.S dollars

place the following words in a binary search tree. add the words to the tree in the order given. lust gluttony greed sloth wrath envy pride

Answers

The binary search tree for the given words (lust gluttony greed sloth wrath envy pride) can be seen as attached.

Running the Python code referenced the attached binary search tree will produce results as follows:

value: envy, count: 1

value: gluttony, count: 1

value: greed, count: 1

value: lust, count: 1

value: pride, count: 1

value: sloth, count: 1

value: wrath, count: 1

search lust, result: (1, 1)

search gluttony, result: (2, 1)

search greed, result: (3, 1)

search sloth, result: (2, 1)

search wrath, result: (3, 1)

search envy, result: (3, 1)

search pride, result: (3, 1)

What is the binary search tree?

The binary search tree is an advanced algorithm used for analyzing the node, its left and right branches, which are modeled in a tree structure and returning the value. The binary search tree is devised on the architecture of a basic binary search algorithm; so, it enables faster lookups, insertions, and removals of nodes.

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place the following words in a binary search tree. add the words to the tree in the order given. lust

Using the diagram below, classify the angle pair ∠CDL and ∠FDE

Using the diagram below, classify the angle pair CDL and FDE

Answers

Answer:

Best shot would be with vertical angles.

It wouldn't be adjacent angles because the two angles don't have an overlapping side.

It also can't be complementary/supplementary angles because they don't add up to 90* or 180* degrees.

However, Angle CDL creates vertical angles with Angle FDE with Angles FDC and EDL.

Hope that helps.

plz help. 100 points!!!

plz help. 100 points!!!

Answers

Answer:

I think you need to subtract by whatever you divide it by.

Step-by-step explanation:

^^^

Answer:

I AGREE!! :))

Step-by-step explanation:

54 ÷ 6 x (12-4) + 2 =​

Answers

Answer:

3

Step-by-step explanation:

1. 54÷6 =9

2. (12-4)=8

3. 9-8 = 1

4. 1+2 = 3

5. I hope this helps it's pretty simple oh and 3 is your anansw.Also you can you your calculator

Answer:

a=72\(\frac{2}{3}\)

Step-by-step explanation:

56/6*(12-4)+2=n

56/6*8+2-2=n-2

56/6*8/8=(n-2)/8

x=9\(\frac{1}{3}\)

x=(n-2)/8

y=74\(\frac{2}{3}\)

y=n-2=a

a=72\(\frac{2}{3}\)

I beeen working on this assignment for 2 hours so if uur good with these stay with me and help please/ Also answer this

I beeen working on this assignment for 2 hours so if uur good with these stay with me and help please/

Answers

Answer:

the answers are 10(x+15)+20(x+30) and 10x+150+20x+600 and 30x+750

Step-by-step explanation:

the first one becuze that what it would look like if written out then the second one becuze that what it would look like if you distributed the 10 and the 20 that outside the parentheses then the third option because you would then combined like numbers so you would do 10x + 20x to get 30x and 600 + 150 to get 750

hope this help please give brainlist

Answer:

The ones  with asterisks below are correct

Step-by-step explanation:

10 days times (x minutes reading/per day + 15 minutes writing/per day)

+ 20 days times (x minutes reading/per day + 30 minutes writing/per day)

= 10(x+15) + 20(x+30) *****

= 10x + 10*15    +    20x + 20*30

= 10x + 150 + 20x + 600  *****

= 30x + 750 *****

Hope this helps, but have to go now.

corresponding sides of similar triangles are 4cm and 3metres .What is the enlargement factor 'k'?​

Answers

Answer:

\(k = 75\)

Step-by-step explanation:

Given

Corresponding sides: 4cm and 3m

Required

Determine the enlargement factor

This is calculated as:

\(k = \frac{New}{Old}\)

So:

\(k = \frac{3m}{4cm}\)

Convert to cm

\(k = \frac{3*100cm}{4cm}\)

\(k = \frac{300cm}{4cm}\)

\(k = \frac{300}{4}\)

\(k = 75\)

The following linear system is to be solved using a
substitution method.
x = 4y – 94
3x + 8y = 218
After the initial substitution, the resulting expanded
equation would be
A. 12y – 282 +8y = 218
B. 3x + 32y – 94 = 218
C. 3x + 32y – 752 = 218
D. 12y-94 + 8y = 218

Answers

Answer:

m=\frac{1}{4}  D. 12y-94 + 8y = 218

Step-by-step explanation:

Answer:

Answer= A

Step-by-step explanation:

equation (1) x=4y-94

equation (2) 3x+8y=218

step 1: for substitution method sub x in the second equation.

3(4y-94)+8y=218

step2: take rid of the bracket by multiplying it by 3.

12y-282+8y=218

(this is the initial expanding result which is answer A)

The answer is not B or C because as they have both letters x and y the did not use substitution method, which will have a one letter result.The answer is not D because they did not multiply -94 by three when expanding the bracket.

I need help with this

I need help with this

Answers

i cannot help with all this but 16 would be 33 ft

A function h(x) has an average rate of change equal to 7 on the interval 5 ≤x≤9. If h(5)=12, then which
of the following must be the value of h(9)?
(1) 28
(2) 36
(3) 40
(4)52

Answers

The required value of h(9) must be 40 which is the correct answer would be option (3).

The function h(x) has an average rate of change of 7 on the interval 5 ≤ x ≤ 9. This means that, on average, the output of the function increases by 7 for every unit increase in the input.

We are given that h(5)=12, which means that the function has an output value of 12 when the input is 5.

To find the value of h(9), we can use the average rate of change to calculate the expected increase in the function's output over the interval 5 ≤ x ≤ 9.

Since the average rate of change is 7, we expect the function's output to increase by 7 × (9-5) = 28 over this interval.

So, the expected value of h(9) is:

⇒ 12 + 28 = 40.

Therefore, the required value of h(9) must be 40.

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based on the graph how many tiles are im figure 0

based on the graph how many tiles are im figure 0

Answers

For figure {0}, the number of tiles will be equal to 2.

What is a mathematical function, equation and expression?          

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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help me please i’ll give you brainly thingy

help me please ill give you brainly thingy

Answers

Answer:

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

because 8/10 divided by 1/5 equals 4

how do I know what goes on the top number line and on the bottom number line?

Please explain this
I don't want the answer but how you get the answer and what number goes on the top and bottom of the 2 number lines, and how do you know what number goes there (on the number line).

how do I know what goes on the top number line and on the bottom number line?Please explain this I don't

Answers

Answer:hmm I don’t fully understand what you mean because there is no bottom of the number line it started at zero so all you have to do is fill the line in.

Step-by-step explanation:

9514 1404 393

Answer:

  get a clue from the problem statement, figure out what you need to help you solve the problem

Step-by-step explanation:

You need to read and understand the entire problem. Different parts of it give you different clues as to how to arrive at appropriate number lines.

Here are some of them:

groups of 3 red cups and 2 blue cups are circled, telling you that 3 red corresponds to 2 blue, and that this combination is one batcheach number line has 4 tick markspart b asks for the number of blue associated with 12 red (so you might want to make sure the numbers on the red number line go that high)part c asks for the number of reds associated with 6 blues (so you might want to make sure the blue numbers go that high)the questions are about "batches", so the tick marks may want to correspond to batches in some way

The double number line is a tool, just as any diagram is a tool to help you solve a problem. You choose the way you draw it so that it is of help to you in answering the questions asked.

Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth

Answers

If Boris has finished 43% of his run on the treadmill, it means that 43% of 99 minutes have gone by. To calculate this, we can multiply 99 by 0.43 to find the number of minutes:

99 minutes * 0.43 = 42.57 minutes

Rounding to the nearest tenth, we can say that approximately 42.6 minutes have gone by.
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