Find the limit of the function f(x, y) = x²y/x² + y² at point (0,0) along the path: [(√yl. y) ∈ R² | y ∈ R}.

Answers

Answer 1

The given path [(√y, y) ∈ R² | y ∈ R] is 0. To find the limit of the function f(x, y) = (x^2y) / (x^2 + y^2) at the point (0, 0) along the given path,

we substitute the path's coordinates into the function and evaluate the limit as (x, y) approaches (0, 0) along that path.

The given path is [(√y, y) ∈ R² | y ∈ R].

Substituting these coordinates into the function:

f(√y, y) = (√y)^2 * y / (√y)^2 + y^2

         = y^1.5 / y + y^2

         = y^1.5 / (y(1 + y))

         = y^0.5 / (1 + y)

Now, let's evaluate the limit as y approaches 0:

lim(y->0) (y^0.5 / (1 + y))

We can apply direct substitution to find the limit:

lim(y->0) (0^0.5 / (1 + 0))

        = 0 / 1

        = 0

Therefore, the limit of the function f(x, y) = (x^2y) / (x^2 + y^2) at the point (0, 0) along the given path [(√y, y) ∈ R² | y ∈ R] is 0.

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Related Questions

The table shows ordered pairs of the function. What is the value of y when? A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12. –20 –8 8 48
I need this quick;-;

The table shows ordered pairs of the function. What is the value of y when? A 2-column table with 6 rows.

Answers

Answer:

-8

Step-by-step explanation:

i checked it out on ... and it was negative eight

Answer:

B: -8

Step-by-step explanation:

edg2021

Just plug 8 into the equation.

The table shows ordered pairs of the function. What is the value of y when? A 2-column table with 6 rows.

DAILY MATH QUESTIN!
CAN YOU SOLVE IT?

DAILY MATH QUESTIN!CAN YOU SOLVE IT?

Answers

Answer:

2

Step-by-step explanation:

you solve the parentases first which equals 12 and then you take 2 times 12 which is 24 and 48 divided by 24 is 2

Answer:

288

Step-by-step explanation:

Start with what's in parentheses: 9 + 3 = 12Plug 12 in: 48 ÷ 2(12)48 ÷ 2 = 24Plug 24 in: 24(12)24(12) = 24 × 12 = 288

I hope this helps!

If 7.3 is subtracted from y, the result is less than 3.4. Find range of values of y​

Answers

Answer:To find the range of values of y that satisfy the inequality, we can solve it algebraically as follows:

Subtract 7.3 from both sides: y - 7.3 < 3.4

Add 7.3 to both sides: y < 10.7

Therefore, the range of values of y is any number less than 10.7. We can write this using interval notation as (-infinity, 10.7) or using set-builder notation as {y | y < 10.7}.

Tell whether each relationship is a function

Tell whether each relationship is a function

Answers

Answer:

This is not a function

Step-by-step explanation:

There are multiple x coordinates so if you put this on a graph then try to do the vertical line test it will fail resulting in this not being a function.

How are the characters developed in the passage? 1. Through their actions 2. Through dialogue 3. Through description 4.through flashback (History)

Answers

Answer:

1

Step-by-step explanation:

Characters are developed in the passage through their actions. Therefore, option A is correct.

What are the characters in a passage?

Characters are the people, animals, or entities portrayed in a literary work such as a passage, story, or novel. They are often the main focus of the narrative and drive the plot forward.

A character can be developed through various literary techniques such as actions. Their traits, motivations, and relationships with other characters help to create a deeper understanding of the story and its themes.

Well-developed characters often feel like real people, with complex personalities, histories, and emotions, which helps to engage the reader and create a sense of empathy or connection. Therefore, option A is correct.

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find the x-coordinates of the inflection points for the polynomial p(x) = x 5 /20 − 5x 4 /12 + 2022/ π .

Answers

The inflection points occur at x = 0 and x = 5.

How to find the x-coordinates of the inflection points?

To find the x-coordinates of the inflection points for the polynomial p(x) = \(x^5/20 - 5x^4/12\) + 2022/π, follow these steps:

1. Compute the second derivative of p(x):
  First derivative: p'(x) =\((5x^4)/20 - (20x^3)/12\)
  Second derivative: p''(x) = \((20x^3)/20 - (60x^2)/12 = x^3 - 5x^2\)
2. Set the second derivative equal to zero and solve for x:
\(x^3 - 5x^2 = 0\)
 \(x^2(x - 5) = 0\)

3. Find the x-coordinates where the second derivative is zero:
  x = 0 and x = 5

These x-coordinates are the inflection points for the polynomial p(x) = \(x^5/20 - 5x^4/12\) + 2022/π. So, the inflection points occur at x = 0 and x = 5.

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What is Y=2x+5 y=3x-1 system by substitution

Answers

Answer:

x=6 , y=17

Step-by-step explanation

3x-1=2x+5

    +1   -2x

x=6

plug in 6 for x to solve y



An airplane was flying at 368 feel. It ascended 250 feet. What is its elevation now?

Answers

Answer:

118 feet.

Step-by-step explanation:

have a great day:)

Answer:

618

Step-by-step explanation:

I need help with this

I need help with this

Answers

Answer:

y = -2x + 3

Step-by-step explanation:

help i don’t understand what this is

help i dont understand what this is

Answers

Answer:

s 3i I mean it's 3

Step-by-step explanation:

it is say what is the square root of 15 so what gives you 15 3

the last digit of the heights of statistics students were obtained as part of an experiment conducted for a class. use the following frequency distribution to construct a histogram. what can be concluded from the distribution of the​ digits? specifically, do the heights appear to be reported or actually​ measured?

Answers

The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.

Frequency Distribution:

Digit Frequency

0 3

1 5

2 9

3 5

4 3

5 4

6 4

7 4

8 2

9 1

From the distribution of the digits, it appears that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.

The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements. For example, the frequency of the digit '2' is more than twice as high as the frequency of the digits '1' and '3', which is not likely to occur in a set of actual measurements.

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Let A be the set of integers that are multiples of 3 between 1 and 15 inclusive and B be the set of even natural numbers up to and including 20. Find A∩B

Answers

After comparing the two sets, we find that 6 and 12 are the common elements of A and B. Therefore, the intersection of A and B is {6, 12}.

The set A is the set of multiples of 3 between 1 and 15 inclusive which are 3, 6, 9, 12, and 15.  The set B is the set of even natural numbers up to and including 20. The set B is {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}.To find A ∩ B, we must determine the elements that A and B have in common. The common elements of A and B are 6 and 12. Thus, the intersection of A and B, A ∩ B, is {6, 12}. To find the intersection of sets A and B, we look for the common elements in the two sets. The set A is the set of multiples of 3 between 1 and 15, while the set B is the set of even natural numbers up to and including 20.

Therefore, we have A = {3, 6, 9, 12, 15} and B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. The intersection of the two sets A and B is the set of elements they share in common. Therefore, we have to look for elements that appear in both sets. After comparing the two sets, we find that 6 and 12 are the common elements of A and B. Therefore, the intersection of A and B is {6, 12}.

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If i buy a disc which costs $16,30, there's a 10% discount. how much i'm i going to pay?

Answers

The price we have to pay for the disc after 10% discount is 1467 dollars.

What is percentage ?

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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Will mark brainliest if you answer correctly and include all the steps! Please hurry I really need you guys to!

Will mark brainliest if you answer correctly and include all the steps! Please hurry I really need you

Answers

Answer:

please repost

Step-by-step explanation:

picture is both blurry and upside down making it difficult to answer quickly. I'd love to help but currently the exponents are unclear :)

(the
graph shows the units of power f(t) after t years
units of Power
100 + lifespan of commucation Statellite
-
30.
60
Describe the intercepts
on the graph.
2.0
years
2 4 6 8 10 hil

(thegraph shows the units of power f(t) after t yearsunits of Power100 + lifespan of commucation Statellite-30.60Describe

Answers

at x = 0, y = 100, y-intercept

meaning at 0 years, at the very beginning of functioning, the satellite had 100 units of power.

at y = 0, x = 10, x-intercept

meaning, at year 10, the satellite had 0 units of power, already out of power.

Complete the table of values. Please help!

Complete the table of values. Please help!

Answers

Answer:

Step-by-step explanation:

Where we have "x" must replace for the number shown on table

We have for "x" tha numbers: 0; 1; 2; 3; 4 and 5

Equation:

1.y = x+4

y = x + 4

For x = 0

y = x + 4

y = 0 + 4

y = 4

For x = 1

y = x + 4

y = 1 + 4

y = 5

For x = 2

y = x + 4

y = 2 + 4

y = 6

For x = 3

y = x + 4

y = 3 + 4

y = 7

For x = 4

y = x + 4

y = 4 + 4

y = 8

For x = 5

y = x + 4

y = 5 + 4

y = 9

So:

x     y

0    4

1     5

2    6

3    7

4    8

5    9

I hope help you.

Simplify (x - y + 1) - (x + y - 1).
-2y+2
2y - 2
-2x + 2y
O2x - 2y + 2

Answers

Answer:

-2y +2

Step-by-step explanation:

(x - y + 1) - (x + y - 1)

Distribute the minus sign

(x - y + 1) - x - y + 1

Combine like terms

x-x -y-y +1+1

-2y +2

Answer:

2y+2

Step-by-step explanation:

Write the linear equation y=−34x+3 in standard form.

Answers

Answer:

34x+y=3

Step-by-step explanation:

Standard Form: ax+by=c.

y=-34x+3

y-(-34x)=3

y+34x=3

34x+y=3

x²-2x=8
x² - 2x - 8 = 0
x² - 2x - 4x = 0
(x - 2) (x - 4)=0

x - 2 =0 therefore x = 2
or
x - 4 =0 therefore x = 4​

Answers

Answer:

x=4   x = -2

Step-by-step explanation:

x²-2x=8

Subtract 8 from each side

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

x^2 -2x  -8=0

What two numbers multiply to -8 and add to -2

-4*2 = -8

-4+2 = -2

(x-4) (x+2) =0

Using the zero product property

x-4 =0   x+2 =0

x=4   x = -2

fill in the blank. _____sample
The population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random.
Example—An airline company wants to survey its customers one day, so they randomly select 555 flights that day and survey every passenger on those flights.
Why it's good: A cluster sample gets every member from some of the groups, so it's good when each group reflects the population as a whole.

Answers

it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

What is intra-cluster sample?

A cluster sample is a sampling technique where the population is divided into clusters or groups, and a subset of clusters is selected at random to form the overall sample. In this type of sampling, all members of the selected clusters are included in the sample.

In the given example, the airline company selects 555 flights as clusters and surveys every passenger on those flights. Each flight represents a cluster, and by selecting random flights, the company includes every passenger on those selected flights in the survey.

This cluster sampling approach is suitable when each group or cluster is representative of the overall population. It is useful when it is impractical or costly to sample every individual unit within the population, but the selected clusters are expected to reflect the characteristics of the entire population.

Cluster sampling allows for more practical data collection, particularly when dealing with large populations or geographically dispersed units. However, it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

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what is multiplicative inverse of -11/17​

Answers

Answer:

The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1. The multiplicative inverse of 'a' is denoted by a-1 or 1/a. ... Dividing a number by itself is equivalent to multiplying it by its multiplicative inverse . Hence, 5 ÷ 5 = 5 × 1/5 = 1.

Step-by-step explanation:

Mark as brainliiest please...

sir

Answer:

it's -17/11

Step-by-step explanation:

A multiplicative inverse or reciprocal for a number a, denoted by 1/a or a⁻¹, is a number which when multiplied by a gives the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a.

Here it's -11/17 x -17/11 =1

A. 33
B. 11
C. 22
D. 66

A. 33 B. 11C. 22D. 66

Answers

Answer:

B

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

The median is 1/2 ( b1+b2)  where b1 and b2 are the lengths of the bases

3x = 1/2(27+39)

3x = 1/2(66)

3x = 33

Divide each side by 3

3x/3 = 33/3

x=11

x plus 2.7 is greater than or equal to 9.4

Answers

Answer:

X >= 6.7

Step-by-step explanation:

So first of all, what you need is write out the equation from the given prompt

x + 2.7 >= 9.4
Next, what you really want to do is

Subtract 2.7 both side
x >= 9.4 - 2.7
x >= 6.7

Which of the numbers below is less than 48.975? Select all that apply. A) 48.9 B) 48.98 C) 48.963 D) 49​

Answers

The correct answers would be both A and C

Answer:

A. 48.9'

C. 48.9663'

a child sits on a fiberglass moose fastened 8.8 meters from the center of a merry-go-round platform that is rotating once every 7 seconds. what is the child's speed while sitting on the moose?

Answers

Answer:

\(\frac{88\pi}{35}\) m/s

Step-by-step explanation:

The circumference is \(8.8(2)(\pi)=17.6\pi\) meters.

So, the speed is \(\frac{17.6\pi}{7}=\frac{88\pi}{35}\) m/s.

You purchased a​ five-pack of new light bulbs that were recalled because ​% of the lights did not work. What is the probability that at least one of your lights is​ defective?.

Answers

The probability that at least one of the lights is defective is 0.2661 .

in the question ,

it is given that

the total number of bulbs in the pack of new light bulbs is (n) = 5

percent of bulb that did not work is  = 6%

probability that lights did not work is (p) = 0.06

probability that lights work is (q) = 1 - 0.06 = 0.94

let x be the number of defective lights

So ,the probability that at least one of your lights is​ defective

is P(x ≥ 1) = 1 - P(x<1)

= 1 - P(x = 0)

By Binomial Probability

= 1 - ⁿCₓ*(p)ˣ*(q)ⁿ⁻ˣ

= 1 - ⁵C₀*(0.06)⁰*(0.94)⁵⁻⁰

= 1 - 1*1*(0.94)⁵         ...because ⁵C₀ = 1

= 1 - (0.94)⁵

= 1 - 0.7339

= 0.2661

Therefore , The probability that at least one of the lights is defective is 0.2661 .

The given question is incomplete , the complete question is

You purchased a​ five-pack of new light bulbs that were recalled because ​6% of the lights did not work. What is the probability that at least one of your lights is​ defective ?

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What is the exact value of sin 120° ? Use a double-angle identity.

Answers

Answer:

\(\frac{\sqrt{3}}{2}\)

Step-by-step explanation:

Sine is positive in the second quadrant, so:

\(\sin \frac{240^{\circ}}{2}=\sqrt{\frac{1-\cos 240^{\circ}}{2}} \\ \\ =\sqrt{\frac{1.5}{2}} \\ \\ =\sqrt{3/4} \\ \\ =\frac{\sqrt{3}}{2}\)

What is the exact value of sin 120 ? Use a double-angle identity.

The position of a particle moving along the y axis has a position given by y=0. 20+8. 0t−10t2. Is there a time interval during which the particle is not moving?

Answers

At t = 0.4, the velocity of the particle is zero. This indicates that the particle is momentarily at rest at this time.

To determine whether there is a time interval during which the particle is not moving, we need to examine the velocity of the particle. The velocity of the particle is the derivative of its position with respect to time.

The given position function is y = 0.20 + 8.0t - 10t^2.

To find the velocity function, we take the derivative of the position function with respect to time (t):

v(t) = d/dt (0.20 + 8.0t - 10t^2)

= 8.0 - 20t

The velocity function v(t) represents the rate of change of the position of the particle with respect to time. If the velocity is zero at any point in time, it means the particle is momentarily at rest.

Setting the velocity function equal to zero, we have:

8.0 - 20t = 0

Solving for t, we find:

20t = 8.0

t = 0.4

So, at t = 0.4, the velocity of the particle is zero. This indicates that the particle is momentarily at rest at this time.

Therefore, there is a time interval during which the particle is not moving, specifically at t = 0.4. Before and after this time point, the particle is in motion either upward or downward along the y-axis.

It's worth noting that we should consider the full domain of the position function (y) to determine if there are any other time intervals during which the particle is not moving. In this case, the given function does not specify any constraints on time, so the time interval t = 0.4 is the only time interval during which the particle is at rest.

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Which functions are symmetric with respect to the origin?

y = arcsinx and y = arccosx
y = arccosx and y = arctanx
y = arctanx and y = arccotx
y = arcsinx and y = arctanx

Answers

Answer:

The correct option is;

y = arcsinx and y = arctanx

Step-by-step explanation:

The given options are;

1) y = arcsinx and y = arccosx

Here, we have at the origin, where x = 0,  arccosx ≈ 1.57 while arcsinx = 0

Therefore arccosx does not intersect arcsinx at the origin for it to be symmetrical to arcsinx or the origin

2)  y = arccosxy and y = arctanx

Here arctanx = 0 when x = 0 and arcos x = 1.57 when x = 0 therefore, they are not symmetrical

3) y = arctanx and y = arccotx

Similarly, At x = 0, arccotx = 1.57 therefore, they are not symmetrical

4) y = arcsinx and y = arctanx

Both functions arcsinx and arctanx pass through the origin and their shapes are similar but inverted as they go from negative to positive.

The function are symmetric with respect to the origin is y = arcsinx and y = arctanx and this can be determined by using the trigonometric property.

The following steps can be used in order to determine which functions are symmetric with respect to the origin:

Step 1 - Check all the options given in order to determine which functions are symmetric with respect to the origin.

Step 2 - Substitute (x = 0) in option a), that is:

\(\rm y = sin^{-1}(0)=0\)

\(\rm y = cos^{-1}(0)=1.57\)

Step 3 - Substitute (x = 0) in option b), that is:

\(\rm y = cos^{-1}(0)=1.57\)

\(\rm y = tan^{-1}(0)=0\)

Step 4 - Substitute (x = 0) in option c), that is:

\(\rm y = tan^{-1}(0)=0\)

\(\rm y = cot^{-1}(0)=1.57\)

Step 5 - Substitute (x = 0) in option d), that is:

\(\rm y = tan^{-1}(0)=0\)

\(\rm y = sin^{-1}(0)=0\)

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a campus performance series features plays, music groups, dance troops, and stand-up comedy. the committee responsible for selecting the performance groups includes three students chosen at random from a pool of volunteers. this year the volunteers came from a variety of majors. however, the three students for the committee were all music majors. does this fact indicate there was bias in the selection process and that the selection process was not random? explain.

Answers

NO , this fact does not indicate that there was bias in the selection process and that the selection process was not random.

This fact does not indicate that there was bias in the selection process and that the selection process was not random unless we know the number of different subject majors among the thirty volunteers.

It is possible that out of 30 volunteers , 20  can be from music majors and the rest 10 are majors from other subjects.

so in this case it is possibility for the process to be random and for the three students in the committee to all end up being music majors.

Therefore , by the given information it can be said that the selection process  was random and unbiased.

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