Evaluate the limit, using L'Hôpital's Rule if necessary. lim x3/9ex/5
x->[infinity]
The limit to be evaluated is
lim x3/9ex/5
x->[infinity]
By direct substitution we have the following. lim x3/9ex/5
x->[infinity]
Thus, the direct substitution results in --Select-- form.

Answers

Answer 1

The limit of the ratio is equal to infinity, i.e.,

lim\(x^{3/9}e^{x/5\) = ∞

x->∞

is ∞.

To evaluate the limit, we can use L'Hopital's Rule, which states that if the limit of the ratio of two functions is of the indeterminate form 0/0 or ∞/∞, then the limit of the ratio is equal to the limit of the ratio of their derivatives (if the latter limit exists).

Applying L'Hopital's Rule to the given limit, we get:

lim \(x^{3/9}e^{x/5\) = lim\((3x^{2/9})e^{x/5\)

x->∞ x->∞

Again applying L'Hôpital's Rule, we get:

lim\((3x^{2/9})e^{x/5\) = lim\((6x/9)e^{x/5\)

x->∞ x->∞

One more time applying L'Hopital's Rule, we get:

lim (6x/9)\(e^{x/5\)= lim\(6e^{x/5} / 9\)

x->∞ x->∞

Since the limit of the ratio of the derivatives exists, we can evaluate it directly to get:

lim\(x^{3/9}e^{x/5\) = lim (\(6e^{x/5\)) / 9

x->∞ x->∞

x approaches infinity, \(e^{x/5\) grows much faster than any polynomial function of x.

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Answer 2

The limit to be evaluated is: lim x3/9ex/5, x->[infinity]

By direct substitution, we have:

lim x3/9ex/5

x->[infinity] = infinity/ infinity

This form is indeterminate and L'Hôpital's Rule can be applied to evaluate the limit.

Applying L'Hôpital's Rule, we take the derivative of both the numerator and denominator with respect to x:

lim x3/9ex/5

x->[infinity] = lim (3x2/9) (ex/5) / (5x4/225) (ex/5)

x->[infinity]

Simplifying this expression, we get:

lim x3/9ex/5

x->[infinity] = lim (3/9) (225/x2) (ex/5)

x->[infinity]

As x approaches infinity, the exponential function grows much faster than the polynomial function x3/9, so the limit of ex/5 as x approaches infinity is infinity. Therefore, the overall limit is infinity, and we can write:

lim x3/9ex/5

x->[infinity] = infinity

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Related Questions

Tayler has $320 to pay for dining room chairs. She expects to pay about $80 per chair. Her friend told her that she has 3 that Taylor can have for free.

Complete the equation below to find the total number of chairs that Taylor can get for her dining room. Use c to represent the total chairs.

Answers

If each chair costs 80 bucks, c chairs costs 80c bucks.

She has 3 already.

80(c - 3) = 320 because the total number of chairs is c, but for 3 of the chairs, she doesn't need to pay.

Write an expression for the area of each shape provided. Make sure it’s in simplest polynomial form

Write an expression for the area of each shape provided. Make sure its in simplest polynomial form

Answers

Answer:\(6x^{2} +7x-5\)

Step-by-step explanation:

area of a trapezoid: a= a+b/2 H

so...

5x+7+x+3/2=6x+10/2=3x+5

then take 3x+5 and multiply it by 2x-1

soo... (3x+5)(2x-1) and I used FOIL

so then 6x^2-3x+10x-5

which is equal to 6x^2+7x-5

I hope this helps =)

Last weekend you attended a concert. You spent a total of $180. Twenty percent of the cost was for a parking pass. The rest of the money was used on 5 tickets. How much was each ticket?

Answers

Answer:

The cost of each ticket was $28.80

Step-by-step explanation:

20% of $180 is $36. 180-36=144. Since there were 5 tickets, the total would be $28.80 for each ticket, which was $144 in all.

What is the area of this figure?
9 yd
4 yd
6 yd
4 yd
4 yd
17 yd
9 yd
19 yd

Pls help me , it’s due today

What is the area of this figure?9 yd4 yd6 yd4 yd4 yd17 yd9 yd19 ydPls help me , its due today

Answers

Answer:

267

Step-by-step explanation:

Simplify the expression.
(10 x n) x 7


PLEASEEEE HELP HELP HELP ASAP!!!!!!!!!

Answers

Answer:

70 x 7n

Step-by-step explanation:

is it just distributing the 7 or what

Answer:

70n.

Step-by-step explanation:

Order of Operations

(10 x n) x 7

10n x 7

70n

Sakura solved a fraction division problem using the rule "multiply by the reciprocal." Look at her work. 7 ÷ 2/ 5 1/ 7 × 2/ 5 = 2/35 Did she solve the problem correctly?

Answers

Answer:

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Step-by-step explanation:

A. Yes. She solved the problem correctly.

B. No. She multiplied the dividend by the divisor instead of finding the reciprocal.

C. No. She multiplied the denominators instead of finding a common denominator.

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Her workings

7 ÷ 2/ 5

=1/ 7 × 2/ 5

= 2/35

Dividend=7

Divisor=2/5

The correct working

7 ÷ 2/ 5

=7 × 5/2

=35/2

Answer:

D

Step-by-step explanation:

I got an 100% on the quiz I took with this question :)

Hope I could help good luck on passing!!

The example of a beach ball with a ping pong ball inside of it can be used to imagine the relationship between what two entities?

Answers

The celestial sphere and Earth is the example of a beach ball with a ping pong ball inside of it can be used to imagine the relationship between what two entities.

The heavenly sphere is what Why is this old idea still relevant today?

Ancient people used the celestial sphere to describe the visible universe. Although our understanding of the cosmos has changed, the concept of a celestial sphere is still prevalent because it provides a straightforward perspective on the stars that is useful for navigation.

Which phrase most accurately sums up the celestial sphere?

The entire sky as seen from Earth is portrayed by the celestial sphere. Keep in mind that the celestial sphere is intended to depict the sky as it appears from our planet rather than physical reality.

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How many outfits can be made from five shirts three pairs of pants and two pairs of shoes?

How many outfits can be made from five shirts three pairs of pants and two pairs of shoes?

Answers

Answer:

3*5*2=30

He can make 30 outfits.

Step-by-step explanation:

3*5*2=30

order to have enough for the trip?
2. An aquarium has 29 large fish tanks. A total of 1,423 fish need to be kept in the
tanks. If the owner wants to split the fish into the tanks as evenly as possible,
what is the greatest number of fish that will be in one tank?
al Paleolith I-man division

Answers

50 would be the largest count of fishes that would be in the tanker.

This is because of divide rule.

If the owner wants to keep the equal number of fishes in the tanker, he have to divide the total number of fishes by total number of tankers.

so,

= \(\frac{1423}{29}\)

= 49.

It implies that 27 tankers would have 49 fishes in each of them and rest 2 tankers will adjust the remaining extra 2 fishes in themselves , so they would accommodate 50 fishes in each of them.

As the name implies, division rules in mathematics allow one to determine if a number may be divided by another number without using the actual division procedure. When two numbers can be divided evenly, the quotient is always a whole number and the remainder is always zero.

In accordance with the rule of seven divisibility, if a number is divisible by seven, then "the difference between twice the unit digit of the provided number and the remaining portion of the given number should be a multiple of seven or it should be equal to zero." 798, for instance, may be divided by 7.

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Question 3 (Essay Worth 10 points) (01.04 MC)The elevation of city A is 96 feet below sea level; the elevation of city C is 24 feet below sea level. The elevation of city D is 1 over 4 of the elevation of city C. Part A: Write an expression to represent the elevation, in feet, of city D. (5 points) Part B: Solve the expression and explain why the answer is negative or positive. (5 points)

Answers

Part A: Expression to represent the elevation of city D.

The elevation of city D is 1 over 4 of the elevation of city C. Therefore, the expression to represent the elevation, in feet, of city D is given by;D = 1/4C ------------------- (1)Part B: Solving the expression and determining the signThe elevation of city C is 24 feet below sea level. Therefore,C = -24Substitute the value of C into equation (1);D = 1/4C= 1/4 (-24)=-6Therefore, the elevation of city D is -6 feet, which is negative. This is because the elevation of city D is below sea level.

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9c+(15-t)= ayudaaaaaaaaa ​

Answers

Answer:

baka

Step-by-step explanation:

Answer:

\(9c + 15 - t\)

Step-by-step explanation:

1) you only have to Remove parentheses.

\(9c + 15 - t\)

Therefor, the answer is 9c + 15 - t.

What is the x-intercept for the equations y = 2x + 4

Answers

Answer:

This seems incomplete can you provide more information

Step-by-step explanation:

Hello guys i am in secondary school y8 and need help on my school work due tomorrow please could you help me out. ​

Hello guys i am in secondary school y8 and need help on my school work due tomorrow please could you

Answers

hii!! i used an online calculator so i could help you quicker, but the area is 60, and the height is 12.

hope this helps!! <3

Find the error(s) and solve the problem correctly. Question: Determine the type(s) of the triangle with the given coordinates. X(6,1) Y(-2,-3) Z(0,3)

Find the error(s) and solve the problem correctly. Question: Determine the type(s) of the triangle with

Answers

In the given computation, the error is in solving the distance of XZ. The square of -2 is not -4 for but +4.

The correct computation will be:

\(\begin{gathered} \text{ XZ = }\sqrt[]{(6-0)^2+(1-3)^2\text{ }} \\ \text{ XZ = }\sqrt[]{(6)^2+(-2)^2} \\ \text{ XZ = }\sqrt[]{36\text{ + 4}} \\ \text{ XZ = }\sqrt[]{40} \end{gathered}\)

Therefore, according to the correct calculations, the triangle is an isosceles triangle.

Solve the equation the square root of the quantity x plus 4 minus 3 equals 1 for the variable.

Answers

Answer:

x = 12

Step-by-step explanation:

sqrt(x+4) - 3 = 1

First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.

sqrt(x+4) = 1 + 3

sqrt(x+4) = 4

To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.

(sqrt(x+4))^2 = 4^2

x + 4 = 16

subtract 4 to finish up.

x = 12

Check:

sqrt(12 + 4) - 3 = 1

sqrt16 - 3 = 1

4 - 3 = 1

1 = 1 Check!

A new pet store is offering 12% off for their grand opening! A parakeet originally costs $17. What is the sale price after the discount?

Answers

Let:

Oc = original cost = $17

Sp = Sale price

D = Discount percent = 12% = 12/100 = 0.12

The sale price will be:

\(\begin{gathered} Sp=Oc-0.12\cdot Oc \\ Sp=17-0.12\cdot17 \\ Sp=17-2.04 \\ Sp=14.96 \end{gathered}\)

The sale price is $14.96

The answer is 14.96

12% of 17 is 2.04
17-2.04=14.96

Find the volume of a cone with a diameter of 12m and height of 9m ? A.108 m3 B.1296 m3 C. 324 m4 D.108 m3

Answers

The closest choice is A. 108  which is the right response if the cone's real height is 4.5m rather than 9m.

what is volume ?

The amount of space a three-dimensional object takes up is measured by its volume. It is a numerical assessment of an object's three-dimensional physical dimensions—length, breadth, and height. Cubic units, such as cubic meters, cubic feet, cubic centimeters, or cubic inches, are used to indicate volume. Mathematical equations can be used to determine the formula for calculating the volume of many geometric shapes, including a cube, rectangular prism, sphere, or cylinder.

given

Finding the cone's radius, which is equal to half of its diameter, is the first stage.

radius: (12 m / 2) = 6 m

The capacity of a cone is calculated as follows:

V = (1/3)π\(r^2\)h

In place of the ideals we hold:

V = (1/3)π(\(6m^2\))(9m) (9m)

V = (1/3)π(\(36^2\))(9m) (9m)

V = (1/3)π(324\(m^3\))

V = 108π \(m^3\)

With the aid of a computer, we can roughly convert to 3.14:

V ≈ 108 x 3.14 \(m^3\)

V ≈ 339.12 \(m^3\)

As a consequence, the cone, which has a 12 m diameter and a 9 m height, has a capacity of about 339.12 m3.

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please help, Solve the following system of equations. Show your work.

−2x+5y=−2

4x−10y=4

Solution:

Answers

After solving the system of equation we will get

x = 5y/2 +1  

y = 2/5- 2x/5

First equation is written

−2x+5y=−2

Subtract 5y from both sides.

−2x =−2−5y

The equation is in standard form.

−2x=−5y−2

Divide both sides by −2.

-2x/-2 = -5y-2/ -2

Dividing by −2 undoes the multiplication by −2.

x= −5y-2/-2

​Divide  −2−5y  by −2.

so

x= 5y/2 + 1

Now the second equation is

4x−10y=4

Add 4x to both sides

-10y = 4-4x

The equation is in standard form.

Divide both sides by 10

-10y/10= 4-4x/10

Dividing by 10 undoes the multiplication by 10.

y= 4-4x/10

Divide 4-4x by 10.

so

y= 2/5- 2x/5

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What is a trend line in math.

Answers

Answer:

Determining if a set of points exhibits a positive trend, a negative trend, or no trend at all.

A trend line, often referred to as a line of best fit, is a line that is used to represent the behavior of a set of data to determine if there is a certain pattern.

A dress whose marked price is Rs 360 is sold at a discount of 10%. If the shopkeeper still makes a profit of 20%, the cost of the dress is​

Answers

Answer:

i dont know if this help comment if not

Step-by-step explanation:

10% discount is 360-36=324

20% profit=  288

Bill makes a conjecture that the sum of an odd integer and itself is always an even
integer. Which choice is the best proof of his conjecture?

Answers

Answer:

Step-by-step explanation:

Bill makes a conjecture that the sum of an odd integer and itself is always an eveninteger. Which choice

given f(g(x)): find f(g(4))

given f(g(x)): find f(g(4))

Answers

Answer:

0

Step-by-step explanation:

Hi there!

First, find g(4). Notice how on the first given table, when x=4, g(x)=9. Therefore, g(4)=9.

Then, find f(9). Notice how on the second given table, when x=9, f(x)=0.

Therefore, f(g(4)) is equal to 0.

I hope this helps!

Find the perimeter of the following quadrilateral.
Write your answer as a mixed number in simplest form.
Be sure to include the correct unit in your answer.

Find the perimeter of the following quadrilateral.Write your answer as a mixed number in simplest form.Be

Answers

Answer:

Plus all the fractions together .

Which equals to 35/4 cm

Step-by-step explanation:

hope it helps you !!

The perimeter of the quadrilateral is P = 8 3/4 cm

Given data:

The perimeter of a quadrilateral is the sum of the lengths of all its sides. A quadrilateral is a polygon with four sides. The formula for finding the perimeter of a quadrilateral depends on the specific type of quadrilateral.

So, the sides of the quadrilateral is represented as:

AB = 3 1/2 cm

BC = 2 cm

CD = 1 4/5 cm

DA = 1 9/20 cm

So, the perimeter is P = 3 1/2 cm + 2 cm + 1 4/5 cm + 1 9/20 cm

On simplifying ,

P = 3.5 cm + 2 cm + 1.8 cm + 1.45 cm

P = 8.75 cm

Hence , the perimeter is P = 8 4/3 cm

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log (8x + 5) = 1 + log (x-4)

Rewrite the given equation without logarithms. Do not solve for x.

Answers

The given equation is rewritten as 8x + 5 = 10(x - 4), using the logarithmic property log a + log b = log(ab) and simplifying further.

To rewrite the given equation without logarithms, we will use the following logarithmic identity:

log(a) + log(b) = log(ab)

First, we simplify the right-hand side of the equation using this identity

log(x - 4) + 1 = log(10) + log(x - 4)

log(x - 4) + log(10) - log(x - 4) = 1

log(10) = 1

Now, we simplify the left-hand side of the equation

log(8x + 5) = log(10) + log(x - 4)

log(8x + 5) - log(10) - log(x - 4) = 0

Finally, we combine the logarithmic terms on the left-hand side:

log[(8x + 5)/(10(x - 4))] = 0

Exponentiating both sides of the equation, we get:

(8x + 5)/(10(x - 4)) = 1

This simplifies to

8x + 5 = 10(x - 4)

We can now solve this equation for x to get the value of x that satisfies the original logarithmic equation.

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Plz help due tomorrow

Plz help due tomorrow

Answers

Answer:

2/5y and -0.2y

-6 and -2

Step-by-step explanation:

Here, we want to select the pair of like terms

To do this, we finish the evaluation of the expression

2/5y + 1/5x - 0.2y -6+ (-2)

We have the two y’s together

2/5y and -0.2y

-6 and -2

1
Susan is buying a subscription to a book company. The function c 45 +3.75m describes the
cost of the yearly subscription, c, in terms of the number of books, m, she orders.
What is the appropriate domain for the function?

Answers

Answer:

C: in terms of the number of books, m, she orders.

Step-by-step explanation:

x(dy/dx) 3y=2x^5; y(x)=1/4x^5 cx^-3, y(2)=1

Answers

The solution after integration is  for y(x) is:\(y(x) = (1/4) x^{(-3)} x^5 - (1/3) e^{(3x)} + (1/3) e^(6)\)

Describe integration.

Finding the integral, or total value, of a given function, is the subject of the area of mathematics known as integration. Finding a function's rate of change entails the differentiation procedure in reverse.

To handle issues like determining the area under a curve, figuring out the volumes of solids in revolution, resolving differential equations, and simulating physical processes, integration is employed in many branches of mathematics, science, and engineering.

Antiderivatives and numerical integration are the two basic methods for determining a function's integral. In contrast to numerical integration, which uses mathematical techniques to approximation the integral, antiderivatives entail finding a function whose derivative is identical to the original function.

How to prove it ?

To find the solution for y(x) given the differential equation X(dy/dx) + 3y = 2x^5, we can use the method of integrating factor. The integrating factor for this equation is given by e^(3x), so we can multiply both sides of the equation by this factor:

\(e^{(3x)} X \frac{dy}{dx} + 3e^{(3x)} y = 2x^5 e^{(3x)}\)

Integrating both sides with respect to x, we get:

\(e^{(3x)} y = (1/3) x^6 + C\)

where C is the constant of integration. To find the value of C, we use the initial condition y(2) = 1:

\((1/3) e^{(6)} + C = 1\)

Solving for C, we get:

\(C = 1 - (1/3) e^{(6)}\)

Finally, substituting C back into the equation for y, we get:

\(y(x) = (1/3) e^{(3x)} x^6 - (1/3) e^{(3x)} + (1/3) e^{(6)}\)

So the general solution for y(x) is:

\(y(x) = (1/4) x^{(-3)} x^5 - (1/3) e^{(3x)} + (1/3) e^{(6)}\)

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A taxi costs $25.20 for 36 miles. How much does the taxi cost per mile?

Answers

Answer:

$0.7

Step-by-step explanation:

$25.20 ÷ 36 = $0.7 per mile

Answer:

Step-by-step explanation:

0,7

A box contains 6 bags of Doritos and 4 bags of Cheetos. Another box contains 5 cans of Coke and 3 cans of Pepsi. If you randomly pick one thing out of the first box and one thing out of the second box, what is the probability you will end up with Doritos and Coke?


A 2/5


B 1/4


C 1/2


D 3/8

Answers

Answer:

Step-by-step explanation:

okay so basically 6+4=10 so the probability of doritos is 3/5 and 5+3=8 so the probabliliy is 5/8. I think the answer is A. but i 100% could be wrong, im sorry if i am

The probability you will end up with Doritos and Coke is; P(Doritos and Coke) = 0.375

How to find the probability?

We are told the components of the box are;

6 bags of Doritos

4 bags of Cheetos

Second box contains;

5 cans of Coke.

3 cans of Pepsi.

Probability of picking doritos in first box = 6/10

Probability of picking coke in second box = 5/8

Thus;

P(Doritos and Coke) = 6/10 * 5/8

P(Doritos and Coke) = 0.375

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A city known for its temperature extremes started the day at -5 degrees Fahrenheit. The temperature increased by 78 degrees Fahrenheit by midday, and then dropped 32 degrees by nightfall. What expression can you write to find the temperature at nightfall?

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Starting temperature = - 5°F

Temperature at midday =increase in temperature by 78°F = (starting temperature + 78°F)

Temperature at nightfall = decrease in temperature by 32°F = ( temperature at midday - 32°F)

Temperature at midday:

(-5°F + 78°F) = 73°F

Temperature at nightfall:

(Temperature at midday - 32°F)

(73°F - 32°F) = 41°F

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