CALCULUS: Which of the following functions grows the fastest as x goes to infinity?
A. 2^x
B. ln(x)
C. sin(x)
D. x^20 (I put this my first try & got it wrong)
I believe D is the right answer, but I got it wrong. Can someone please tell me why?
Answers
Answer:
It is A. 2^x
Step-by-step explanation:
For relative rates of growth, we know: Log < Poly < Exponential.
This rules out B, C, and D quickly. Although, if you do L'Hôpital's rule, it might seem like A & D are very comparable. However, if you continually took the derivative of 2^x and x^20, eventually x^20 would equal zero, while 2^x would still be a variable. So, you would have:
[tex]\lim_{x \to \infty} \frac{2^{x}}{0} =[/tex] ∞
When the limit of x as it approaches infinity is infinity, then f(x) grows at a faster rate than g(x).
Also, by looking at the graph (which is attached), you can see that 2^x grows faster than x^20.
Related Questions
I have to do a math test what is 8 + (7 + 1) 2 ÷ 4 ⋅
Answers
Answer:
8
Step-by-step explanation:
taking my points back because you answered with spam.
What is the circumference of the circle?
Answers
Answer:
c=40.192
Step-by-step explanation:
c=2pir
c=2*pi*6.4
c=12.8pi
c=12.8*
c=40.192
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Answers
Answer:
d≈21.99
Step-by-step explanation:
the arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence
Answers
Given:
In an arithmetic sequence,
[tex]a_1=2[/tex]
[tex]a_i=a_{i-1}-3[/tex]
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
[tex]a_i=a_{i-1}+d[/tex] ...(i)
Where, d is the common difference.
We have,
[tex]a_i=a_{i-1}-3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]d=-3[/tex]
The sum of first i terms of an arithmetic sequence is:
[tex]S_i=\dfrac{i}{2}[2a+(i-1)d][/tex]
Putting [tex]i=335,a=2,d=-3[/tex], we get
[tex]S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)][/tex]
[tex]S_{335}=\dfrac{335}{2}[4+(334)(-3)][/tex]
[tex]S_{335}=\dfrac{335}{2}[4-1002][/tex]
[tex]S_{335}=\dfrac{335}{2}(-998)[/tex]
On further simplification, we get
[tex]S_{335}=335\times (-499)[/tex]
[tex]S_{335}=-167165[/tex]
Therefore, the sum of the first 335 terms in the given sequence is -167165.
Solve the equation by completing the square.
a2 - 14a - 32 = 0
Answers
Answer:
a=16,-2
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term. Solve for a by using this term to complete the square.
Molly and Melissa swam laps during practice.
• Together they swam 25 laps.
Melissa swam 5 more than 3 times as much as Molly.
Write an equation for this situation. Use a variable to represent the number of laps for Molly
How many laps did Molly swim?
Answers
Helppppp !!!!!!
During a 20 kilometer hike, Deana consumed 3 3/4 quarts of water.
What was Deana's average water consumption in quarts per kilometer?
Answers
Answer:
16.7
Step-by-step explanation:
The amount of water consumed is 334 quarts
The distance is 20km
Therefore the average water consumption can be calculated as follows
= 334/20
= 16.7
Hence the consumption rate is 16.7 quarts/km
MULTIPLE CHOICE QUESTION A car travels 120 miles in 2 hours. It goes an average of South East direction. What is its velocity? 60 mph south east 45 mph 45 mph south east 60 mph
Answers
Answer:
60 miles per hour southeast.
Step-by-step explanation:
We are told that the car is moving southeasternly, so that answers the question right off the bat. The car is moving 120 miles per 2 hours. We need to know how much it moves in one hour though, so we must divide hours and miles by 2. We ger 60 miles per hour.
Velocity will be 60 mph southeast.
What is the difference between velocity and speed?The distance that an item travels in a unit of time is referred to as its speed. It merely takes into account the size of the item and ignores its orientation. Speed is referred to as a scalar quantity in this way. When referring to velocity, however, it is said that velocity is the rate at which displacement changes. A vector quantity, that is.
Given distance traveled by car is 120 miles in 2 hours. Since speed is distance divided by time.
Speed = 60 mph
Also, there is a given direction which is southeast.
Therefore, the velocity of the car will be 60 mph southeast.
Learn more about velocity here:
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can anyone help me with #1?
Answers
Answer:
x = 16.1 in
Step-by-step explanation:
Using sin law
sin44 / x = sin98/ 23in
x = 16.1 in (nearest tenth)
Any hot you have an index card with a number 1 through 10 written on them find how many of the 10 possible numbers you can pick match describe event and drag and drop each of the numbers into the contact Box the order the event is most 1 likely to happen to most likely of happened 8 you will pick one card at random
Answers
6
Solve the inequality. Graph the solution.
11.3 > b /4.3
The solution is
Answers
Step-by-step explanation:
Multiply to remove the fraction, then set equal to
0 and solve.
Inequality Form:
b<48.59
Interval Notation:
(−∞, 48.59)
The solution of the inequality 11.3 > b /4.3 is b< 48.59 along with the number line.
Given Inequality:
11.3 > b /4.3
To solve the inequality 11.3 > b / 4.3,
Multiply both sides of the inequality by 4.3 to eliminate the fraction:
11.3 * 4.3 > (b / 4.3) * 4.3
48.59 > b
The solution to the inequality is b < 48.59.
This means that any value of b that is less than 48.59 will satisfy the inequality.
To graph the solution, indicate that b is less than 48.59 by using an open circle at 48.59 and shading the line to the left of the open circle to represent all the values that satisfy the inequality.
Learn more about Inequality here:
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The leading brand of cosmetics in the US had about 20% of the total sales in the industry. The total
sales were $2.6 billion. What was the leading brands sales? Show your work.
Answers
Answer:
The answer is $520,000,000
Step-by-step explanation:
To find twenty percent of the total $2.6 billion, all you need to do is multiply 2.6 billion * 20%
2.6, 000,000,000 * 20% (or 1/5) is 520,000,000
Since this answer is reasonable, the answer is $520,000,000
Need help on this question
Answers
Answer:
Step-by-step explanation:
arc between cars = 360°/25 = 14.4°
θ = 14.4° × π/180 ≅ 0.2512 radian
r = 150/2 = 75 ft
s = rθ = 75×0.2512 = 18.84 ft
area of circle = πr² = 75²π ≅ 17,662.5 ft²
area of sector = 17,662.5/25 = 706.5 ft²
The attendance at a baseball game was 400 people. Adult seats sold for $15 and children seats sold for $10. Total ticket sales were $4560. How many of each type of ticket were sold?
Answers
Answer:
112 adult and 288 children
Step-by-step explanation:
x= adult seats
y= children seats
15x + 10y = 4560
x + y = 400 --> y=400-x
so plug 400-x for y in the other equation
15x + 10(400-x)= 4560
now solve this equation
15x + 10(400-x)= 4560 --> 15x + 4000-10x= 4560 --> 15x -10x = 560 --> 5x=560 --> x = 560/5 --> x= 112
now plug in 112 for this equation (x+y=400) --> 112+y=400 --> y= 288
This month Joe spent 1/2 of his salary on food and 1/3 on rent. What part of his salary did he spend? Simplify the fraction if possible.
Answers
Answer:
the answer is 5/6
Step-by-step explanation:
1/2 + 1/3
1 =3 + 2=1 5
x
-- + --- = ---
2 x 3 = 6
WILL MARK BRAINLIEST!! Just help me out with number 2 please. :)
Here is an inequality: -2x > 10.
1. List some values for x that would make this inequality true.
Answer: Any negative number above -5, like -6, -7, etc.
2. How are the solutions to the inequality -2x ≥ 10 different from the solutions to
-2x > 10? Explain your reasoning.
Answers
9514 1404 393
Answer:
-5 is included in the solution set of the first, but not the second
Step-by-step explanation:
The solution to -2 ≥ 10 is x ≤ -5. The solution to -2x > 10 is x < -5. The difference is that x = -5 is included in the solution set of the first inequality, but is not included in the solution set of the second inequality.
When plotted on a number line, the former inequality has a solid dot at -5, indicating that point is included. The latter inequality has an open dot (circle) at -5, indicating that point is not included. (Both plots are shaded to the left of the dot.)
What is m∠1?
There is a horizontal line. Point B and D are lies on the line. There is one point C which is joined with point B and D to form a triangle CBD. The angle BCD is 70 degree. The angle CBD is denoted by 2. The supplementary angle of 2 is denoted by angle 1 which is line formed with segment BC. The line formed obtuse angle with CD is 130 degree.
A. 130°
B. 70°
C. 60°
D. 120°
Answers
Answer:
i think b
Step-by-step explanation:
HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
Answers
ill mark brainlist plss help
Answers
Answer:
25 in²
Step-by-step explanation:
formula for area of a triangle:
1/2(bxh)
1/2(5x10)
1/2(50)
25
Answer:
D. [tex]25^{2}[/tex]
Step-by-step explanation:
please help :) thanks !
Answers
Answer:
Step-by-step explanation:
b
If each cube in the rectangular prism measures 1 cubic inch, what is the volume of the prism?
A.
40 cubic in
B.
168 cubic in
C.
84 cubic in
D.
144 cubic in
Answers
hmm, how many cubes are there?
length times width times height
we have 6 cubes long, 6 wide and 6 tall
6*6*6=216 cubes
each is 1 cubic feet
216 times 1=216
216 cubic feet
A is answer
Help out thankssssssssss !!!!!!
Answers
Answer:
x =20?
Step-by-step explanation:
I set them equal to each other
Answer:
it says the answer s t u v
George worked on his science project for 5/12 hours on monday and 3/4 hour on tuesday. How much longer on tuesday did georege than on monday
Answers
Answer:
2/8 hours
Step-by-step explanation:
Plz give me brainlyist
Chandler, Jamal, Allison, and Qi are given the following problem. In 1982, Wayne Gretsky set a record for the greatest number of hockey goals in one season with 92 goals. If a player has scored 60 goals this season and averages 2 goals per game, how many additional games must he play to break the record? Each student writes an inequality to represent the situation. Chandler wrote 60 + 2g ≥ 92 Jamal wrote 60 + 2g > 92 Allison wrote 60 + 2g < 92 Qi wrote 60 + 2g ≤ 92 Whose inequality is CORRECT? A. Qi B. Chandler C. Allison D. Jamal
Answers
Answer:
The correct answer is B.
Step-by-step explanation:
Since Chandler, Jamal, Allison, and Qi are given the following problem: "In 1982, Wayne Gretsky set a record for the greatest number of hockey goals in one season with 92 goals. If a player has scored 60 goals this season and averages 2 goals per game, how many additional games must he play to break the record? ", And each student writes an inequality to represent the situation:
Chandler wrote 60 + 2g ≥ 92
Jamal wrote 60 + 2g> 92
Allison wrote 60 + 2g <92
Qi wrote 60 + 2g ≤ 92
To determine whose inequality is correct, the following calculation must be performed:
92 - 60 = 32
32/2 = 16
Chandler: 60 + 2x16 ≥ 92
Thus, Chandler wrote the correct option.
HELP ME PLEASE ❗❗❗❗
What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
Answers
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
:P
-10=-8+6(w-5) simplify your answer as much as possible
Answers
Answer:
i hope this helps
Step-by-step explanation:
-10 = -8+6(w-5) (reorder)
-8+6(w-5) = -10 (add 8 to both sides)
6(w-5) = -2 (divide both sides by 6)
w-5 = -1/3 (add 5 to both sides)
w = 14/3 or 4 2/3
Emma is driving at a constant speed. She drives 4 miles in 5 minutes. If she continues to drive at the same speed, how many miles will she drive in 15 minutes? Use a proportion to solve.
A:3 miles B:12 miles C:20miles D:60miles
Answers
Answer:
D. 60 Miles
Step-by-step explanation:
Consider triangles CBD and BDE and answer the questions that follows
2.1 Which side is common in both triangles?
2.2 What can be concluded about the heights of A CBD
and A BDE? Give a reason for your answer.
2.31 Using your answers from 2.1 und 2.2 above complete
the following statements:
2.3.1 Area of A CBD
2.3.2 Area of ABDE
2.4 What can be concluded about the area of A CBD and
ABDE?
Answers
Answer:
Step-by-step explanation:
∠ABD ≅ ∠BDE..... (given).... (1)
m∠ABD + m∠CBD = 180°... (straight line ∠'s)... (2)
From equations (1) & (2)
m∠BDE + m∠CBD = 180°....(3)
m∠BDE + m∠CDB = 180°... (straight line ∠'s)... (4)
From equations (3) & (4)
m∠BDE + m∠CBD = m∠BDE + m∠CDB
m∠CBD ≅ m∠CDB.. (Proved)
A hardware store received 2.5 tons of
lumber. What is the weight of the
lumber in pounds?
A 50,000 pounds
® 25,000 pounds
5,000 pounds
D 2,500 pounds
Answers
Answer:
5000 pounds
Step-by-step explanation:
Hello There!
There are 2000 pounds in 1 ton
So to convert tons to pounds we multiply by 2000
2.5x2000=5000
So 2.5 tons is the equivalent if 5000 pounds
ez one cus im lazy so give it a shot and 1st right = brainle
Answers
Answer:
d
Step-by-step explanation:
Answer:
For The Number 6 Its A
For The Number 7 The Volume is 400