give an example of a function that is discontinous at one and only one point in its domain but is continous at every other point

Answers

Answer 1

An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function f(x) = x^2.

This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous. At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.

The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.

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Related Questions

Write the
slope-intercept form of the equation of
the line that passes through the point (1, 2) and
has the slope of 6.

Answers

2=6x1+b this is slope intercept form

Simplify (-3x^4) (-4x^2)

Answers

Remove all -
Proceed with equation

12x^6

Final answer

Step-by-step explanation:

(-3x⁴)(-4x²)

as multiplication is commutative (that means the sequence of the factors is irrelevant), we get

-3×-4×x⁴×x²

we can combine everything of the same type (constants or variable names).

-3×-4 = 12

remember, -×- = +

x⁴×x² = x⁶

remember, when multiplying terms with the same base variable, we can simply add the exponents.

why ? because an exponent is a short way of saying that the base variable has to be multiplied by itself that many times.

e.g.

a³ = a×a×a

a⁷ = a×a×a×a×a×a×a

a³×a⁷ = a×a×a × a×a×a×a×a×a×a = a¹⁰

that's why.

so, the complete simplified expression is

12x⁶

pls do this qwick

What is the product of (−23)(18)(−4)?

−1,656
−322
74
1,656

Answers

Answer:

1656

Step-by-step explanation:

Answer: 1656

Step-by-step explanation:

just trust me, that's the answer! I did the same question.

Math geometry,

GIVEN

Answers

The SSS congruence theorem is used to prove that triangles MAH and THA are congruent to each other. See proof below.

How to Apply the SSS Congruence Theorem?

"SSS" stands for side-side-side congruence theorem, which says that given the criteria that two triangles both have three corresponding sides that are equal or congruent to each other, both triangles are congruent.

The proof below shows how we can apply the SSS to prove that triangles MAH and THA are congruent to each other.

Statement Reason

1. MA ≅ TH 1. Given

2. MH ≅ AT 2. Given

3. AH ≅ HA 3. Reflexive property of congruence

4. ΔMAH ≅ ΔTHA 4. SSS congruence theorem

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sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants she packed. The total number of pairs of pants and shirts was 16

Answers

Answer:

She packed 6 pairs of pants and 10 shirts.

Step-by-step explanation:

Say the number of pants is x. Then, the number of pants is 2x-2. Now you have the equation:

x+ (2x-2)=16

Solving this equation gives x=6.

Therefore, she packed 6 pairs of pants and 10 shirts.

URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7

Answers

The first blank as required to be filled in the task content should be filled with; two.

The second blank as required to be filled in the task content should be filled with; 134.1 in³.

What is the volume of the cone?

According to the information given; the diameter of the beachball is; 8 inches. Therefore, it's radius is half that; 4 inches.

On this note, the volume of the beachball which is spherical in shape given by the formula;

Volume of a sphere = (4/3)πr³ where;

Radius, r = 4;

Therefore, volume of beachball is;

4/3 π (4)³ = 256π / 3.

Also, the volume of the cone which is given by the formula;

Volume of a cone = (1/3) π r² h

where; Radius, r = 4 and Height, h = 8.

Therefore, volume of the cone is;

(1/3) π (4²) × 8 = 128π / 3.

On this note, by dividing the volume of beachball by that of cone; we have that;

( 256π / 3 ) / ( 128π / 3 ) = 2.

On this note, the cone will fit into the beachball about 2 times.

Also, the volume of the cone given that; π = 22 / 7 can be evaluated as;

( 128 × 22 ) / ( 7 × 3 )

= 134.1 in³.

Answers

Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map f: X --> X such that f(x) = x- 1 is an example of continuous map is one to one and honto but is not a homemorphism .

What is a bijective function?

A function f: A --> B is said to be bijective or bijection if it satisfies both injective (one-to-one function) and surjective (over-function) properties. Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map

f : X--> X such that f(x) = x- 1 ; x∈X (domain)

Now, we show that it is bijective, so

One to One : let x₁ and x₂ belongs to X such that f(x₁) = f(x₂) we have to show x₁= x₂

f(x₁) = f(x₂) => x₁ - 1 = x₂ - 1

=> x₁ = x₂ -1 + 1

=> x₁ = x₂

So, f(x) is one to one.

Onto : let y be a element of X ( co-domain) We can show that there exists x∈A such that f(x)=y. Choose x= f⁻¹(y) and so f(f⁻¹(y))=y. So for all y∈B, there exists an x∈A such that f(x)=y. Therefore, it is onto. Thus, f(x) is one to one and onto and continus( due to polynomial nature) i.e it is a continuous bijection from X to itself, but it is not a

homeomorphism, since the image of N is not open.

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Indicate whether a binomial distribution is a reasonable probability model for the random variable X. give your reasons in each case.
joey buys a virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

Answers

The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.

How to identify binomial distribution model?

The conditions for binomial distribution are;

1: The number of observations n must be fixed.

2: Each observation must be independent.

3: Each observation must represent one of two outcomes ("success" or "failure").

4: The probability of "success" p must be the same for each outcome.

Now, we are given the statement;

Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.

Secondly, we can say that there could be success by winning a price or failure by not winning the price.

Each weekly observation is independent.

The probability is the same for each outcome.

Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.

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how do you prove 6^7-6^6+6^5 is divisible by 31

Answers

the same digit. Please note that in order to check the last digit of a5
a
5
you just can ignore all digits but the last one. Thus, you can asume that a
a
has a single digit. You only have to check the fifth power of the numbers 0 to 9. It’s easy and fun, if I may add

Step-by-step explanation:

I don't know if this is valid but

We can think of this problem like

(6^7-6^6+6^5)/31 = x

Where x is a whole number so 6^7-6^6+6^5 is divisible by 31

Multiply each side with 31 :

6^7-6^6+6^5 = 31x

We can turn 6^7 into 6^5 x 6^2

We can also turn 6^6 into 6^5 x 6

So the equation turns into this :

(6^5 x 6^2) - (6^5 x 6) + (6^5 x 1) = 31x

We can factor out the 6^5 out of the left side of the equation, which turns into :

(6^5) x (6^2 - 6 + 1) = 31x

Which is also :

(6^5) x (31) = 31x

Divide each side with 31

6^5 = x

X is obviously a whole number

Calculate the difference and enter below. 3-9

Answers

Answer: -6

Step-by-step explanation: Since 9 is being subtracted from 3, we know that it will be a negative number. So, 9-3 = 6, and a greater number subtracted from a smaller number is a negative number. So, that results in this being -6. I hoped this helped.

[tex]3-9[/tex]

[tex]3+(-9)[/tex]

[tex]=\fbox{-6}[/tex]

[tex]3+(-9)[/tex] on a number line:

(100 points plus brainliest) A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordered pair (4, 3) is on the graphed line

what is the price of 1 pound of potatoes? SHOW YOUR WORK

Answers

Answer: $0.75

Step-by-step explanation:

-We know that the line must also contain the point (0,0), as 0 pounds of potatoes would cost $0. Thus we can find the slope of the line and write an equation:

slope = Δy/Δx = (3-0)/(4-0) = 3/4

y = (3/4)x

(The y-int (aka b) is 0 since the line passes through (0,0))

Plugging in 1 yields $0.75

Answer:

$0.75 per pound

-------------------------------------------------------

Proportional relationship equation:

y = kx, where k-constant of proportionality

Given point (4, 3).

Use its coordinates to find the value of k:

3 = 4kk = 3/4k = 0.75

This is representing the price of 1 pound of potatoes.

Claim: all natural numbers are either even or odd. Proof: By induction. Base case:0 is even, since 0 = 2.0. Now suppose that n - 1 is either even or odd, and we must show that n is either even or odd. Case 1: If n - 1 is even, then n - 1 = 2k for some k, so n = 2k + 1, showing n must be odd. Case 2: If n - 1 is odd, thenn - 1 = 2k +1 for some k, so n = 2k + 2 = 2(k+1), showing n must be even. Is this proof correct?
• Yes • No

Answers

No. The proof is wrong.

Here we are asked to prove all Natural numbers are either even or odd.

Natural numbers start from 1 to infinity.

Hence to prove by mathematical induction, we need to take the base case to be n = 1.

here, 1 = 2X0 + 1, therefore 1 is odd

Then we need to assume that for any integer m < n, m is either even or odd.

Now n > 1

Therefore,

n -1 > 0

Hence n - 1 will be a natural number.

Hence by our earlier assumption where any number smaller than is either even or odd

n - 1 has to be either even or odd.

case 1

here n - 1 is odd

if n - 1 is odd then

n-1 + 1 is a sum of two odd numbers, hence n is even

Case 2- If n - 1 is even

then, n-1 + 1 is a sum of an even and n odd number hence n is odd

Therefore n will either be even or odd.

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Please help will mark Brainly

Answers

Answer:

Below

Step-by-step explanation:

The solution set is the point(s) where the two plotted graphs intersect:

A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33

Answers

The 95% confidence interval for this situation is (0.95, 9.71).

What is the Standard deviation?

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The formula for Confidence Interval for Population Mean When Population Standard deviation is known

[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]

α for 95% confidence level = (100-95)/100 =0.05

[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025

[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96

σ = 20

95% Confidence Interval for Population Mean When Population Standard deviation is known