when x=1,2,3,.... find limit x->infinity
choice
a. 0
b. 1
c. 2
d. 3
f. 4
help me!!!

When X=1,2,3,.... Find Limit X->infinitychoice A. 0b. 1c. 2d. 3 F. 4help Me!!!

Answers

Answer 1

Let y = √x, so the limit can be rewritten as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{\sqrt{y^6+y^2}}{y^2+3} - \frac{\sqrt{y^4+1}}{y+4}\right)[/tex]

Now,

[tex]\sqrt{y^6+y^2} = \sqrt{y^2\left(y^4+1\right)} = y\sqrt{y^4+1}[/tex]

so we can rewrite the limit further as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{y}{y^2+3} - \frac1{y+4}\right)\sqrt{y^4+1}[/tex]

Combine the rational terms:

[tex]\dfrac y{y^2+3} - \dfrac1{y+4} = \dfrac{y(y+4)-(y^2+3)}{(y^2+3)(y+4)} = \dfrac{4y-3}{(y^2+3)(y+4)}[/tex]

Then in the limit, we get

[tex]\displaystyle \lim_{y\to\infty}\frac{(4y-3)\sqrt{y^4+1}}{(y^2+3)(y+4)} = \lim_{y\to\infty}\frac{(4y^3-3y^2)\sqrt{1+\dfrac1{y^4}}}{y^3+4y^2+3y+12} \\\\ = \lim_{y\to\infty}\frac{\left(4-\dfrac3y\right)\sqrt{1+\dfrac1{y^4}}}{1+\dfrac4y+\dfrac3{y^2}+\dfrac{12}{y^3}} = \boxed{4}[/tex]


Related Questions

Solve for x.
5x + 3 – 2x = 24
X = [?]

Answers

[tex]\\ \sf \longmapsto 5x+3-2x=24[/tex]

[tex]\\ \sf \longmapsto 5x-2x+3=24[/tex]

[tex]\\ \sf \longmapsto 3x+3=24[/tex]

[tex]\\ \sf \longmapsto 3x=24-3[/tex]

[tex]\\ \sf \longmapsto 3x=21[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{21}{3}[/tex]

[tex]\\ \sf \longmapsto x=7[/tex]

Answer:

x = [7]

Step-by-step explanation:

5x + 3 - 2x = 24

Combine like terms

5x - 2x + 3 = 24

Subtract 5x - 2x

3x + 3 = 24

Subtract 3 from both sides

3x = 21

Isolate the variable

x = 21/3

x = 7

Jami bought 4 cookies that cost $1.45, each. She paid with 6 one-dollar bills. how much change does Jami recive?

Answers

Answer:

$0.20

Step-by-step explanation:

4 x 1.45 = $5.80

6.00 - 5.80 = 0.20

Answer: $0.20

Step-by-step explanation:

Do 4 *$1.45 = $5.80

This is how much her total was.

She gave $6 in cash.

Subtract.

6-5.80=$.20

Is 512 is not a perfect square​

Answers

Answer:

A perfect square is a number that can be expressed as the product of two equal integers.

The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work.

Try these steps first:

A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.

Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.

All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

Let's try it...

Step 1:

What is the last number of 512? It is this number: 512. The answer is 2. Is 2 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: YES, 2 is in the list of numbers that are never perfect squares. The number 512 is NOT a perfect square and we can stop here as there is not need to complete the rest of the steps.

ASAP
Which of the following points is in the solution set of y > -x^2 + 5?
A.) (2, 4)
b.)(1, 3)
c.)(0, 5)
wrong = reported
ty

Answers

The answer is C.) (0, 5)

Explaintion is in the pictures

I believe this is the answer if it isn't I'm sorry for wasting your time by answering.

Hope this helps!

Find the value of x. Round to the nearest tenth.Find the value of x. Round to the nearest tenth.

Answers

Answer:

x = 55.6

Step-by-step explanation:

In order to find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

x is the hypotenuse

the opposite is 19

So we have

sin 20 = 19/x

x = 19/sin 20

x = 55.55

We have the final answer as

x = 55.6 to the nearest tenth

Hope this helps you

Answer:

x = 55.6

Step-by-step explanation:

sin(90°-x)=-root 3/2
what value of x satisfies the equation

Answers

Answer:

x = 30 degrees

Step-by-step explanation:

sin( 90 -x) = cos(x)

cos (30) = [tex]\frac{\sqrt{3} }{2}[/tex]

The value of x from the trigonometric relation is x = 210°

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin (-θ) = -sin (θ)

csc (-θ) = -csc (θ)

cos (-θ) = cos (θ)

sec (-θ) = sec (θ)

tan (-θ) = -tan (θ)

cot (-θ) = -cot (θ)

In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

In the third quadrant going anti-clockwise, only tan is positive.

In the fourth quadrant going anti-clockwise, only cos is positive

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

sin ( 90° - x ) = -( √3/2 )   be equation (1)

On simplifying the equation , we get

sin 60° = √3/2

Substituting the values in the equation , we get

sin ( 90° - x ) = - sin ( 60° )

And , sin (-θ) = -sin (θ)

Substituting the values in the equation , we get

sin ( 90° - x ) = sin ( - 60° )

On further simplification , we get

( 90° - x ) = ( - 60° )

Adding x on both sides of the equation , we get

x - 60° = 90°

Adding 60° on both sides of the equation , we get

x = 150°

x = π/3 + 90 + 2πn

x = 2π/3 + 90 + 2πn

Therefore , the value of x is 150° or 210°

Hence , the value of x is 210°

To learn more about trigonometric relations click :

https://brainly.com/question/14450671

#SPJ2

The opposite angles of a cyclic quadrilateral are (3x + 10)
and (2x + 20)°. Find the angles.

Answers

Just check your work so

( 2x - 9) x ( x + 5 )

Answers

[tex]2x \times x + 2x \times 5 - 9 \times x - 9 \times 5[/tex]

[tex] {2x }^{2} + 10x - 9x - 45 [/tex]

[tex] {2x}^{2} + x - 45 [/tex]

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\boxed{x=14}[/tex]

Reorder the terms:

[tex]-9 + 2x = 5 + x[/tex]

Solving

[tex]-9 + 2x = 5 + x[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

[tex]-9 + 2x + -1x = 5 + x + -1x[/tex]

Combine like terms: [tex]2x + -1x = 1x[/tex]

[tex]-9 + 1x = 5 + x + -1x[/tex]

Combine like terms: [tex]x + -1x = 0[/tex]

[tex]-9 + 1x = 5 + 0\\-9 + 1x = 5[/tex]

Add '9' to each side of the equation.

[tex]-9 + 9 + 1x = 5 + 9[/tex]

Combine like terms: [tex]-9 + 9 = 0[/tex]

[tex]0 + 1x = 5 + 9\\1x = 5 + 9[/tex]

Combine like terms: [tex]5 + 9 = 14[/tex]

[tex]1x = 14[/tex]

Divide each side by '[tex]1[/tex]'.

[tex]x = 14[/tex]

Simplifying

[tex]x = 14[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

How many films does he have ?

Answers

Answer:

85 films

Step-by-step explanation:

10 + 20 + 25 + 20 + 10

= 85 films

answered by g a u t h m a t h

How much is $100 USD in cross water dollars

Answers

Answer:

62034.74

Step-by-step explanation:

Answer:

62034.74  use a converter

Step-by-step explanation:

Which equation represents a parabola that has a focus of (0,0) and a directix of y = 2?​

Answers

Answer: D

Step-by-step explanation:

[tex]a=0,\ b=0,\ k=2\\equation\ of\ the\ parabola:\\\\y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\\\y=-\dfrac{x^2}{4}+1 \\\\x^2=-4(y-1)\\\\Answer\ D[/tex]

Solve for a.
-4a – 2a – 7 = 11
a =
[?]
Not a fraction answer

Answers

Answer:

sorry for point

plz

plz

plz

plz

Answer:

Hello,

Answer: a=-3

Step-by-step explanation:

[tex]-4a-2a-7=11\\\\\Longleftrightarrow\ -6a-7=11\\\\\Longleftrightarrow\ 6a=-7-11\\\\\Longleftrightarrow\ 6a=-18\\\\\Longleftrightarrow\ a=-3\\[/tex]

Evaluate -3.28 - (-4.4) + (-p) where p = 9.7

Answers

Answer:

-8.58

Step-by-step explanation:

p = 9.7

=> -3.28 - (-4.4) + (-p)

=> -3.28 - (-4.4) + (- (9.7))

=> -3.28 - (-4.4) + (-9.7)

=> -3.28 - (-4.4) -9.7

=> -3.28 +4.4 -9.7

=> -12.98 +4.4

=> -8.58

Answer:

The evaluated answer for this equation is -8.58

Step-by-step explanation:

We are given a value of p so we will use this value for the equation.

-3.28 - (-4.4) + (-p)

Replace p with 9.7

-3.28 - (-4.4) + (-9.7)

Since there is a double negative in front of 4.4, then that means that we are going to be adding -3.28 to 4.4

1.12 + (-9.7)

Subtract 1.42 from 9.7 because there is negative sign in front of 9.7

-8.58

construct a right-angled triangle ABC where angle A =90 degree , BC= 4.5cm and AC= 7cm. please ans fast........ Very urgent. Pls don't give wrong answers

Answers

Answer and Step-by-step explanation: The described right triangle is in the attachment.

As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:

AC² = AB² + BC²

[tex]AB^{2} = AC^{2}-BC^{2}[/tex]

[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]

[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]

[tex]AB =\sqrt{28.75}[/tex]

AB = 5.4

Then, right triangle ABC measures:

AB = 5.4cm

BC = 4.5cm

AC = 7cm

Find the measure of the missing angles.


b =
C=

Answers

Answer:

Angle C and Angle B 61 degree as Angle 119 is supplementary to angle B and C (180-119=61)

Bob and Carol want to hire Able Refinishing to sand and refinish the dining room floor to match the floor in the living room. Able charges $2.41 per square foot to sand and refinish a hardwood floor. The dining room is rectangular and measures 17 feet 10 inches by 11 feet 9 inches. Find the area of the dining room floor and the cost of the work.

Answers

Answer:

Area = 209.5 ft² (nearest tenth)

Cost = $505 (approximated)

Step-by-step explanation:

Step 1: convert the inches to be in feet by dividing length in inches by 12.

17 feet 10 inches => [tex] 17 + \frac{10}{12} = 17.83 ft [/tex]

11 feet 9 inches => [tex]11 + \frac{9}{12} = 11.75 ft[/tex]

Step 2: Find the area of the floor of the dinning room

Area = 17.83*11.75 = 209.5 ft² (nearest tenth)

Step 3: Find the cost of the work.

Cost = 209.5 ft² × $2.41 = $505 (approximated)

(3-1) (4+2) + 9 - 3 I need help

Answers

Answer:

18

Step-by-step explanation:

(3-1) (4+2) + 9-3 =

2 • 6 + 6 = 12 + 6

= 18

Answer:

[tex]\displaystyle 18[/tex]

Step-by-step explanation:

[tex]\displaystyle (3 - 1)(4 + 2) + 9 - 3 = [(2)(6)] + 9 - 3 = 12 + 9 - 3 = 12 + 6 = 18\:[OR\:21 - 3 = 18][/tex]

G - Grouping Symbols

E - Exponents

M\D - Division & Multiplication [left to right]

A - Subtraction & Addition [right to left OR vice versa]

I am joyous to assist you at any time.

Which expression, in exponential form, is equivalent to 26x3y 47z5r3 A) ( 26x3y 47z5r3 )2 B) (26xy) 1 2 (47zr) 1 2 C) 26 1 2 x 3 2 y 1 2 47 1 2 z 5 2 r 3 2 D) 26x 3 2 y 1 2 47z 5 2 r 3 2

Answers

Answer:

The answer is "all the choices were wrong"

Step-by-step explanation:

Given value:

[tex]\bold{26x^3y 47z^5r^3}[/tex]

In the given question all the choices were wrong because it is not equivalent to given equation:

In choice A) [tex]( 26x^3y 47z^5r^3 )^2[/tex] in the value is whole squared, that's why it is wrong.

In choice B) [tex](26xy)^{12} (47zr)^{12}[/tex] when we open its value it will give different values, that's why it is wrong.

In option C and D( [tex]26^{12} x^{32} y^{12} 47^{12} z^{52} r^{32}[/tex] and [tex]26x^{32} y^{12}47z^{52} r^{32}[/tex]) both values will give different values.  

Answer:

it's C

Step-by-step explanation:

I just did it

At Horatio's machining company, it takes 2 minutes to manufacture each part and 10 minutes to pack all the parts for an order. Write an expression that shows how many minutes it will take to complete an order, assuming there are x parts in an order.

Answers

Answer:

f(x) = 2x + 10

Step-by-step explanation:

Let's call this function f(x), where f(x) is time to get the order ready and x is the number of parts:

f(x) = 2x + 10 Is the expression of this function.

2x is the time to manufacture all parts of the order and 10 min is the time to pack them.

Answer:

2x + 10 is the correct answer :)

PLEASE I REALLY CAN'T THINK OF ANYTHING ELSE
list 2 differences between y = sin x and y = cos x

Answers

Answer:

- sin(x) is the ratio of the opposite leg to the hypotenuse in a right triangle, while cos(x) is the ratio of the adjacent leg to the hypotenuse in a right triangle.

-The graph of y = sin(x) at x = 0 starts at the origin, and then increases, while the graph of y = cos(x) starts at a max, and then decreases.

Here's a 3rd: sin(x) is the cofunction of cos(x), which means that sin(x) = cos(90-x). This also shows that they are different.

If Paul and Steve are the same height and they are both correct, write an equation to represent this relationship. Put Paul's expression on the left side of the equal sign and Steve's expression on the right.

Answers

Answer:

Theresa's height=60 inches

Paul's height= Steve's height=74 inches

Step-by-step explanation:

Theresa has two brothers,Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. If they're both right, how tall is Theresa ?

Let

p=paul's height

s=steve's height

t=theresa's height

Paul's height = Steve's height

p=s

Paul says he is 16 inches shorter than 1 1/2 times Theresa's height

1 1/2 * t -16

=3/2t -16

Steve says he is 6 inches shorter than 1 1/3 times Theresa's height

1 1/3 * t - 6

=4/3t - 6

P=S

3/2t -16 = 4/3t - 6

Collect like terms

3/2t-4/3t= -6+16

9t-8t/6 =10

t/6=10

Cross product

t=60

Theresa's height=60 inches

P=3/2t -16

=3/2(60) -16

=180/2 -16

=90-16

=74 inches

p=s

Paul's height=74 inches

Evaluate ab+bc+ca . If a²+b²+c²=50 and a+b+c=12​

Answers

Answer:

ab+bc+ac=47

Step-by-step explanation:

(a+b+c)=12

Square both sides

a^2+b^2+c^2+2(ab+bc+ac)=144

2(ab+bc+ac)=94

ab+bc+ac=47

Answer:

ab + bc + ca = 47

Step-by-step explanation:

Using the algebraic identity

(a + b + c) = a² + b² + c² + 2(ab + bc + ca) , then

12² = 50 + 2(ab + bc + ca)

144 = 50 + 2(ab + bc + ca) ← subtract 50 from both sides

94 = 2(ab + bc + ca) ← divide both sides by 2

47 = ab + bc + ca

The value of r represents the distance from a point to the pole when plotting
that point in polar coordinates.
A. True
B. False

Answers

Answer:true
Hope this helped

PLEASE HELP ME The graph below shows the distance, y, that a car traveled in x hours:
Rate of Travel
125
100
Distance Traveled
(miles)
75
501
251
0 1 2 3 4 5
Time (hours)
What is the rate of change for the relationship represented in the graph?
о
1
50
O
25
O 25
050

Answers

Answer:

25

Step-by-step explanation:

The graph is going up by 25 each block or point of the way, if im wrong, im sory

The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?

Answers

Answer:

1/6

Step-by-step explanation:

People who answered less than 1/2 were:  2 +  1 + 3 = 6 people.

There are a total of 36 people.

People who answered their calls before the second ring were only 6/36.

When we simplify the fraction, we get 1/6.

So, the answer is 1/6.

Consider the functions F and G in the tables below
PLEASE HELP PLEASE

Answers

Answer:

Option A, As x increases, the rate of change exceeds the rate of f

help me I’m bad with this stuff

Answers

Answer:

(4x10^1)(2x10^4)

=40^1 × 20^4

=800^5

Answer:

8 x 10^5

Step-by-step explanation:

We can start by grouping the powers of ten together and the other numbers together, as you can move numbers around when multiplying:

4 x 2 x 10^1 x 10^4

4 multiplied by 2 is 8, so we can put that in:

8 x 10^1 x 10^4

Next, using the product rule, 10^1 x 10^4 would be ten to the power of the sum of the two exponents, or 10^(4 + 1), which is 10^5.

We will be left with

8 x 10^5

This is in scientific notation, so no further modification is needed.

Find the squares of the following:
1)2a+1 2) 3b+2c 3) 2p²+3q²

Answers

Answer:

1. 4a^2 + 4a + 1

2 9b^2 + 12bc + 4c^2

3 4p^4 + 12p^2q^2 + 9q^4

Step-by-step explanation:

SOMEBODY PLEASE HELP ME ON THIS ; DUE TODAY, i’ll mark u the brainliest

Answers

Answer: Angle Addition Postulate

Step-by-step explanation:

According to the angle addition postulate, the measure of an angle formed by two angles side by side is the sum of the measures of the two angles. It is used to evaluate the measure of an angle formed by two or more angles .

In the given picture, we have ∠MRO and ∠MRS on line SRO.

So, ∠SRO = ∠MRO +∠MRS  [By angle addition postulate]

So the postulate that justify the statement " ∠SRO = ∠MRO +∠MRS" is Angle Addition Postulate.

mrs tay baked some tarts. 25% of the tarts are pineapple tarts and the rest are strawberry tarts. She baked 90 more strawberry tarts than pineapple tarts. How many strawberry tarts did she bake? ​

Answers

Step-by-step explanation:

100 - 25 = 75

75 + 90 = 165

= 165 strawberry .

Other Questions
Help .....plz help....me What is Chuck Andersons favorite style? A. vibrant colors with minimal lighting effects B. dull colors and powerful light effects C. bright colors and powerful light effects D. dull colors and dim lighting effects 1. What historical event is the team investigating? What, if anything, do you alreadyknow about this event (The wreck of the Sultana steamboat)? I need help please help me! I dont understand this I need help with #7 I got no clue what to do Guys pls help me in this coz im very confused in this graph the solution set to the inequality Select the correct answer from each drop-down menu.353025Number of Roses2015105021345XNumber of PlantsAccording to the graph, the relationship between the number of rose plants and the number of roses is pls answer my question please The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random variable ranging from 4 to 10. How is the following decimal written using bar notation? 3.126666666666...3. 1263.1260 3.12603.126 Pls answer my question it is urgent it is Notice writing 5. When it is 8:00 p.m. in the Pacific time zone, what time is it in western Tennessee? In the year 2010, 148 million Americans will be enrolled in an HMOt is the sum of the geometric series ? Is this descriptive or inflectional statistics Consider the formula 4(h-3k)= h+7. (a) Make k the subject of the above formula. (b) If the value of h is decreased by 8, write down the change in the value of k.guys I really need helpplzzzzzz 59,8x60,2 bng bao nhiu 489X96x =degrees Henry, a new human resources coordinator, has been asked to calculate the past month's turnover rate. He has divided the number of people who have left the company during that month (11) by the number of employees hired(10), and then multiplied that by 100. But the number hehas come up with, 110 percent, is way too high anddoesn't make any sense. What should have Henry doneto avoid his error?He should have multiplied the cost toterminate by the cost per hire.He should have multiplied by 10, not 100.He should have divided the number ofemployees hired by the cost to hire them.He should have divided the number of peoplewho have left the company by the averagenumber of employees that month. Simplify 7 to the 6th power 7 to the fifth power. 49 to the 11th power 49 to the 35th power 7 to the 11th power 7 to the 35th power 6x + 7y = 4x + 4y what is x when y is -4 PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!