Guess the value of the limitlim x??(x^4)/4x)by evaluating the functionf(x) = x4/4xfor x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, and 100. Use a graph of f to support your guess.

Answers

Answer 1

The graph should show a horizontal asymptote at y = 1/4 as x approaches infinity. Our guess for the value of the limit of f(x) as x approaches infinity is 1/4.

To guess the value of the limit of f(x) = (x⁴)/(4x) as x approaches infinity, we can evaluate the function for increasing values of x and observe the trend.

When x = 0, the function is undefined as we cannot divide by zero.

For x = 1, f(x) = 1/4.
For x = 2, f(x) = 2.
For x = 3, f(x) = 27/4.
For x = 4, f(x) = 4³/16 = 4.
For x = 5, f(x) = 625/20 = 31.25.
For x = 6, f(x) = 6³/24 = 27/2.
For x = 7, f(x) = 2401/28 = 85.75.
For x = 8, f(x) = 8³/32 = 16.
For x = 9, f(x) = 6561/36 = 182.25.
For x = 10, f(x) = 10³/40 = 25.
For x = 20, f(x) = 20³/80 = 100.
For x = 50, f(x) = 50³/200 = 312.5.
For x = 100, f(x) = 100³/400 = 2500.

From these values, we can see that as x increases, f(x) approaches 1/4. This is because the x in the denominator grows faster than the x^4 in the numerator, causing the fraction to approach zero.

We can also confirm this trend by graphing f(x) using a software or calculator. The graph should show a horizontal asymptote at y = 1/4 as x approaches infinity.

Therefore, our guess for the value of the limit of f(x) as x approaches infinity is 1/4.

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Related Questions

I need help I am really struggling with math

Answers

Answer:

Okay what is it i might be able to help

Step-by-step explanation:

Gabriella made 5 waffles for breakfast. She has 25 strawberries and 15 blueberries to put on top of the waffles. She will put a equal number of berries on each waffle.How many berries will gabrielle put on each waffle?

Answers

She will use 3 blueberries on each and 5 strawberries on each hope this helps <3

randy needs to save 2550$ for a vacation. he has 6 months to save the money. how much money must he save each month?

Answers

Answer:

425

Step-by-step explanation:

2550/6=425

Answer:

425

Step-by-step explanation:

If A = 56° then find C.

Answers

Answer:

124

Step-by-step explanation:

If you are talking about angles, then the answer is 124 degrees. Question is a little open, though.

I hope this helps!

Rule: multiply by 2 Pattern: 3,6,12,24,48 Observation: Observation = something similar about the numbers

Answers

Step-by-step explanation:

This numerical sequence corresponds to a geometric progression, which occurs when there is a multiplication of the sequence numbers for a common reason whose result will always be the successor number of the numerical sequence.

Like for example:

3,6,12,24,48

The common reason for the geometric progression is the number 2, so the first term of the sequence multiplied by 2 will be equal to the second term of the sequence and so on:

3x2 = 6

6x2 = 12

12x2 = 24

24x2 = 48

It is necessary to emphasize that the ratio of a geometric progression will always be constant and will always be a number other than zero.

Find The Area of the parallelogram...

Answers

Answer:

162 ft^2

Step-by-step explanation:

the formula for finding the area of a triangle is [tex]\frac{b*h}{2}[/tex]

the base is 27 and the height is 12

[tex]\frac{27*12}{2}=\frac{324}{2} = 162[/tex]

the area of a triangle is (base X height)/2

(27 X 12)/2 = 324/2 = 162ft^2

-(7p+6)-2(-1-2p)
what is that simplified?

Answers

Answer:

-3p-40

Step-by-step explanation:

-(7p+6)-2(-1-2p)

-7p-42+2+4p

-3p-40

Which Triangle appears to be both right and isosceles?

Answers

Answer: B

Step-by-step explanation: An isosceles right triangle is an isosceles triangle and a right triangle. This means that it has two congruent sides and one right angle. Therefore, the two congruent sides must be the legs.

Answer:

B

Step By Step Explanation:

The corner of the triangle is at 90 degrees making it a right angle. Both legs are congruent and has corresponding angles.

geometry: help needed, it’s urgent!
angle 1 measures 75 degrees, is this table right?

Answers

Answer:

angle 1 and 3 are alternate INTERIOR angles cos they are on the inside of the lines but you were close

The results of the first 100 students who voted are represented in the table. There are still 50 more students left to vote. Based on the early results, how many MORE votes do you expect Dan to get out of the 50 late voters?

Answers

Answer:

1-50

Step-by-step explanation:

The area of circle can be expressed by the
formula A = ar?where r is a radius of circle.
express radius in terms of area of circle.

Answers

9514 1404 393

Answer:

  r = √(A/π)

Step-by-step explanation:

Solve for r. Do this by dividing by the coefficient of the r² term, then taking the square root.

  A = πr²

  A/π = r²

  r = √(A/π)

What is the conjugate of
(-5 + 4i)?

Answers

Answer:

the answer to that is -1i

Step-by-step explanation:

cause if you add negative and positve you get to subtract it and get the sign of the highest number

help me plz plz i need my grades up​

Answers

Answer:

Decimal: 2.1

Fraction: 21/10

Answer:
2.1
Explanation

tysm for whoever helps !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11

Answers

Answer:

21

Step-by-step explanation:

When you simply the fractions down, you will get this

[tex]16 + 5 = 21[/tex]

Hope this Helped

I need an explanation for the problem 4v2=-12v-9. I don't understand why it factors into 4v+3 and 4v+3

Answers

Answer:

The factors are [tex]2v+3,2v+3[/tex].

The factors are not [tex]4v+3,4v+3[/tex]

Step-by-step explanation:

Equation is [tex]4v^2=-12v-9[/tex].

This equation can be written as follows:

[tex]4v^2+12v+9=0[/tex]

Here,

[tex]12v=6v+6v[/tex]

Therefore,

[tex]4v^2+6v+6v+9=0\\2v(2v+3)+3(2v+3)=0\\(2v+3)(2v+3)=0[/tex]

So, the factors are [tex]2v+3,2v+3[/tex].

The factors are not [tex]4v+3,4v+3[/tex]

If g(x) = 2x – 9, determine g(4) – g(1)

Answers

Step-by-step explanation:

g(x) = 2x - 9

g(4) = 2* 4 - 9

= 8 - 9

= - 1

g(1) = 2 * 1 - 9

= 2 - 9

= - 7

Now

g(4) - g(1)

= - 1 - ( -7)

= - 1 + 7

= 6

Hope it will help :)

Can 4(x+2)=10 equal 0

Answers

Answer:

x = 0.5

Step-by-step explanation:

The given expression is :

4(x+2) = 10

Using commutative property at LHS.

4x+8 = 10

Subtract 8 from both sides.

4x+8-8 = 10-8

4x = 2

x = (1/2) = 0.5

So, the value of x is equal to 0.5 instead of 0. Hence, the given expression cannot be equal to 0.

Look at the photo below.

Answers

Answer:

complement, 70; supplement, 160*

Step-by-step explanation:

A set of 25 two digit numbers are listed below 10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98. What is the probability of the sum of the number's digits is odd?

Answers

Answer:

0.48

Step-by-step explanation:

Given the data:

X:

10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98

Sum of each of the numbers :

1, 8, 2, 5, 6, 10, 6, 12, 6, 7, 8, 7, 20, 13, 7, 11, 12, 9, 12, 15, 16, 13, 13, 16, 17

Probability that sum of the number's digit is odd:

Number of odd sum / total numbers

Number of odd sum = 12

Total numbers = 25

12 / 25

= 0.48


Solve and graph the inequality.
7n - 1 > 76

Answers

Answer:

n>11

Step-by-step explanation:

I don't know how to graph this answer, sorry!

The solution of the inequality 7n - 1 > 76 gives n < 11 along with the graph.

Given Inequality:

7n - 1 > 76

To solve the inequality add 1 on both side of inequality as

7n - 1 + 1 > 76 + 1

7n > 77

Now, divide the inequality by 7 as

7n/ 7 > 77/ 7

n > 11.

Therefore, the solution is n > 11.

Learn more about Inequality here:

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y-2=1/2(x-4) in slope intercept form

Answers

Answer:

y = 1/2x

Step-by-step explanation:

y - 2 = 1/2 (x-4)

y = 1/2x - 2 + 2

y = 1/2x

(The y - intercept is 0 because -2 and 2 cancels each other out)

Hope this helps :)

Let me know if there are any mistake!!

The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be

⇒ y = 1/2x

What is equation of line?

The equation of line in slope intercept form is defined as;

y = mx + b

Where, 'm' is slope of line and 'b' is y-intercept.

Given that;

The equation of line is;

y - 2 = 1/2 ( x - 4 )

Now,

We can change the equation of line in slope intercept form as,

y - 2 = 1/2 ( x - 4)

Solve as;

y - 2 = 1/2 x - 1/2 × 4

y - 2 = 1/2 x - 2

Add 2 both side,

y - 2 + 2 = 1/2 x - 2 + 2

y = 1/2 x

Thus, The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be;

⇒ y = 1/2x

Learn more about the equation of line visit:

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− 2/3m = −1/2 solve for m

Answers

Answer:

m=-18

Step-by-step explanation:

-12=2/3m

How many fluid ounces are in 1 quart? With work!

Answers

Answer: 32 fluid ounce = 1 quart

Hey I'm sorry. I don't know if there are any work to show for this but I will try.

1 quart=2pints

2pints=4cups

4cups=32 fl oz

This is all the work I could show for this problem, you really should memorize this though 32 fl oz in a quart, it is very useful real life information :)

In the number 8246315 what sigit is in the ones place​

Answers

Answer:

5

Step-by-step explanation:

The ones place is the one most to the right that isn't after a decimal point.

Answer:

5, since it is all the way to the right

Step-by-step explanation:

if you ever have a big number, the number in thes ones place is ALWAYS on the far right, except if its a decimal !

i hope this helps !! :D

HELP ASAP HELPPP MARKING BRAINLIEST

Answers

The answer is 68 1/8

Answer:

answer is 68 1/8

Step-by-step explanation:

there are 5 red marbles, 7 green marbles, 4 black marbles, and 8 blue marbles in a bag. Find P(not yellow

Answers

Total number of Marbles is = 5 + 8 + 7 = 20

Total number of non-red marbles = 5 + 7 = 12.

P( Not yellow) 12/20 = 3/5.

The answer is 3/5.

Answer:

3/5

Step-by-step explanation:

Multiplying positive and negative fractions how do you do it ​

Answers

Answer:

I GOTCHU BAEE

Step-by-step explanation:

its just like regular negative numbers

but with fractions

see:

-7/12 x 1/2 = -7/24

negative negates the negative

negative negates the positive

positive keeps the positive positive

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents.

(b^4)2

Answers

Answer:

[tex](b^4)^2 = b^{8}[/tex]

Step-by-step explanation:

Given

[tex](b^4)^2[/tex]

Required

Simplify

In indices, we have:

[tex](a^m)^n = a^{m*n[/tex]

So:

[tex](b^4)^2 = b^{4*2}[/tex]

[tex](b^4)^2 = b^{8}[/tex]

uM ANY help pls?
Hopely someone can help!

Answers

Answer:

He made 35% of his shots he did not make 65& of his shots

Step-by-step explanation:

7/20=35%, 20/7=65%

What is the value of the expression 11 - (34.48?
1) 3
O2) 5
O 3) 8
4) 9

Answers

Answer:

-23.48

Step-by-step explanation:

Hoped this helped!!

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