How do I solve this problem? The trouble that I have is evaluating if 2^∞ or ∞³ is larger?
Answers
For large enough x, exponential functions like 2ˣ will always dominate a polynomial of any degree. This is to say the denominator will always be larger than the numerator (again, for sufficiently large x). So the limit in this case would be 0. (I'll leave a link in comments to a variety of answers regarding this detail.)
But if you've been introduced to L'Hopital's rule: we have
[tex]\displaystyle \lim_{x\to\infty}\frac{5x^3+10}{6\times2^x-1} = \lim_{x\to\infty}\frac{15x^2}{6\ln(2)\times2^x} = \lim_{x\to\infty}\frac{30x}{6\ln^2(2)\times2^x} = \lim_{x\to\infty}\frac{30}{6\ln^3(2)\times2^x} = \frac1\infty = 0[/tex]
Related Questions
Find the value of x if 2x-1÷3 is greater than 1-3x÷4 by 1
Answers
[tex]\\ \sf\longmapsto \dfrac{2x-1}{3}-\dfrac{1-3x}{4}=1[/tex]
[tex]\\ \sf\longmapsto \dfrac{4(2x-1)-3(1-3x)}{12}=1[/tex]
[tex]\\ \sf\longmapsto 8x-4-3+9x=12(1)[/tex]
[tex]\\ \sf\longmapsto 17x-7=12[/tex]
[tex]\\ \sf\longmapsto 17x=12+7[/tex]
[tex]\\ \sf\longmapsto 17x=19[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{19}{17}[/tex]
5x-1/3=4
5x-1=12
5x=13
X=2.6
Given f (x) = -x + 2, find f(0).
Answers
Answer:
f(0) =2
Step-by-step explanation:
f (x) = -x + 2
Let x = 0
f(0) = -0+2
f(0) = 2
Answer:
f(0) = 2
Step-by-step explanation:
Substitute x = 0 into f(x)
f(0) = - 0 + 2 = 0 + 2 = 2
Sam ordered 2 tons of crushed stone. How many pounds of crushed stone does she have?
Answers
Answer:
4000
Step-by-step explanation:
1 ton = 2000 pounds
2 tons = ? pounds
Multiply:
2000 × 2 = 4000
There will be 4000 pounds of crushed stone.
Hope this helped.
Sam ordered 2 tons of crushed stone. How many pounds of crushed stone does she have?
S O L U T I O N :Here, we need to convert the tons into pounds to get the desired result
✪ According to the question :
We know that,
1 ton = 2000 pounds
2 tons = 2(1000 pounds) = 2000 pounds
Hence, she have 2000 pounds of crushed stoneHelp please with my geometry
Answers
Because RS + ST=RT
So basically x+3x=5x-4
4x=5x-4
-4x -4x
-1x=-4
x=4
Exercise 5
A bag of corn can feed 50 chickens for 12 days.
a) For how many days will the same bag feed 40 chickens?
b) How many bags of corn are needed to feed 20 chickens for 30 days?
2. Fifteen men build a wall in five days. How long will it take the following
number of men to build the wall?
al one man
b) 10 men
c) 20 men
3. A 3-year-old girl has six sisters. Her youngest sister is 4 years old.
a) How many sisters did she have when she was 1 year old?
Answers
Answer:
Step-by-step explanation:
a) By proportion number of days = 12 * 50/40
= 15 days.
b) Finding the number of bags per day that 1 chicken needs:
50 chickens eat 1 bag in 12 days
so 50 chickens eat 1/12 of a bag in 1 day.
1 chicken eats 1/(12*50) of a bag in 1 day.
20 chickens for 30 days:
20 chickens eats 20(12*50) in 1 day
and in 30 days 20 eat 30*20 / (12*50)
= 1 bag.
2.
a) 5*15 = 75 days
b) (15/10) * 5 = 7 1/2 days.
c) (15/20) * 5 = 3 * 5 /4 = 3 3/4 days.
3. When she was 1 year old her youngest sister was 2 - she had the same number of sisters as when she was 3.
So the answer is 6.
Make a list of professionals who routinely apply geometry in their work.
Answers
Answer:
1. Architects
2. Civil Engineers
3. Astronomers
4. Game Developers
5. Animators
6. Interior Designers
7. Surveyors
8. Designers who use computer-aided design.
Identify the glide reflection rule in the given figure.
Question 8 options:
Translation: (x,y) → (x – 5,y); Reflection across y-axis
Translation: (x,y) → (x,y – 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across x-axis
Answers
Answer:
B
Step-by-step explanation:
The shape clearly is reflected across y axis and the x coordinates remain the same. We can see a change in the y coordinates and the shape has shifted 5 units down. Hence (x, y) -> (x, y-5) and then reflection across y axis is the answer
Answer:
B
Step-by-step explanation:
If n(A) = P and n(B)=q then n(AxB) is (a ) p (b ) q ( c ) p+q ( d ) pq
Answers
By way of example, suppose A = {1, 2, 3} and B = {a, b, c}. Then the Cartesian product of A and B is
A × B = {{1, a}, {1, b}, {1, c}, {2, a}, {2, b}, {2, c}, {3, a}, {3, b}, {3, c}}
That is, each element in A gets a pairing with each element in B, and for each pairing you have n(A) choices for the first element and n(B) choices for the second element.
So if n(A) = p and n(B) = q, then n(A × B) = pq.
how to locate square root 100 on number line
Answers
Answer:
10
Step-by-step explanation:
Answer:
Step-by-step explanation:
First we find the square root of 100(for this we use a calculator)
[tex]\sqrt{100\\}[/tex] = 10
The square root of 100 is 10.
Now locate 10 on a number line.
WHAT IS ANOTHER NAME FOR NATURAL NUMBERS?
PLs answer!
Answers
Answer:
Natural Numbers (N), is also called positive integers, counting numbers, or natural numbers.
✌✌✌✌
Answer:
Another name of natural number is called counting number.
Geometry, please answer question ASAP
Answers
BECAUSE ACCORDING TO THE PERIMETER (TRIANGLE ) FORMULA = B * H / 2.
B = BASE.
H = HEIGHT.
THE HEIGHT IS A VARIABLE VLAUE NEEDED IN ORDER TO ONTINUE TO SOLVE AND EVENTUALLY LEADING TO THE ANSWER (TRIANGLE PERIMETER.
Bridgette bought 9 books about animals, 6 books about outer space, and 3 books about
trains. Each book cost $16. How much did Bridgette spend on the books?
Answers
Answer:
(9+6+3)×16=288
Step-by-step explanation:
add all the books and then multiple by the price of one book to get an answer
I NEED HELP ASAP!!People that now the Answer help me please
Answers
please help:
give an example of an undefined term and how it relates to a circle.
Answers
I need help please ASAP Ik how to do it its easy but I wanna make sure so please help
Answers
Step-by-step explanation:
Answer in attached picture...
hope it helps
Look at this rectangular prism:
If the height is quadrupled, then which of the following statements about its volume will be true?
Answers
Answer:
the new volume Will be 4 times the old volume
Step-by-step explanation:
I have put the photo 3
Find AC (Round to the nearest tenth) PLS HURRY
Answers
Answer:
Does the answer help you?
Find the indicated side of the
right triangle.
45°
y
6
45
Х
y = [?] /
Answers
Answer:
hello dear...
see first of all there's a thm type thing
'' sides opposite to equal angles are equal ''
so here 45 degrees in both sides are equal which leads us that opposite sides are equal as well
so x = 6
now we got value of 2 sides, both are 6 and now applying pythogarus as it is right angle
6^2 + 6^2 = y^2
36+36 = y^2
72 = y^2
y = √72
y = √36*2
y = 6√2
brainliest plssss <33
Tell whether each order pair is a solution of the equation.
1. 2x+y=5 (2,1)
2. 4x-3y=10 (4,3)
helppp pls i don’t understand thisssss
Answers
Answer:
1.) (2,1) is a solution
2.) (4,3) is NOT a solution
Step-by-step explanation:
1.) (2,1)
These are these mean (x,y)
2=x and 1=y
You want to substitute the numbers for the letters in the equation.
so.
2(2)+1=5
4+1=5
5=5, This statement is true so (2,1) is a solution.
2.) Same as above. 4=x and 3=y
4(4)-3(3)=10
16-9=10
7 Does Not Equal 10, Therefore, (4,3) is Not a solution to the equation.
If S=4πr² , find
i) the value of S when r = 10
Answers
Answer:
S = 1256
Step-by-step explanation:
S = 4[tex]\pi[/tex][tex]r^2[/tex]
S = 4[tex]\pi[/tex][tex](10)^2[/tex]
S = 4[tex]\pi[/tex][tex](100)[/tex]
S = [tex]4(314)[/tex]
S = 1256
Answer:
400pi, or 1256.637...
Step-by-step explanation:
S = 4pir^2
S = 4pi(10^2)
S = 4pi(100)
S = 400pi
what is
f(x)= (x-12)(x+1)
in standard form?
Answers
Answer:
x^2-11x-12
Step-by-step explanation:
I use the box method, which makes a 2x2 box. Then you arrange you numbers based on the equation (show in image)
Then you multiply it out and get the equation
F(x)= x^2+x-12x-12
Simplify your equation and you get
F(x)= x^2-11x-12
Which function is the inverse of 6) = 2x+39
ASAP
Answers
Answer:
The inverse is 1/2x - 3/2
Step-by-step explanation:
y = 2x+3
To find the inverse, exchange x and y
x = 2y+3
Solve for y
x-3 =2y+3-3
x-3 = 2y
Divide by 2
1/2x - 3/2 = 2y/2
1/2x - 3/2 = y
The inverse is 1/2x - 3/2
whats a+17-29+17=43-7
Answers
Answer:
a = 31
Step-by-step explanation:
a+17-29+17=43-7
Combine like terms
a+5 = 36
Subtract 5 from each side
a+5-5 = 36-5
a = 31
The bar graph shows the median income for families in the United States from 1993 through 2000.
Which two consecutive years saw the largest increase in median income?
A. 1994–1995
B. 1997–1998
C. 1998–1999
D. 1999–2000
Answers
The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.
Given that
In 1994-1995, the median income is 37,500 and 38,500.In 1997-1998, the median income is 39,700 and 41,000.In 1998-1999, the median income is 41,000 and 42,200.In 1999-2000, the median income is 42,500 and its less.So after analysis, we can conclude that The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.
Learn more about the bar graph here: brainly.com/question/14894834
How many ten-thousands are there in these numerals? (a) 10650 (b) 21540 (C) 36907 (d) 74215 (e) 99999
Answers
Answer:
a
Step-by-step explanation:
10650
it is ten thousand
any way is this choosing or question. in my answer I answer as it is choosing. if it is question let me know in comment. I will answer again in comment
a) There are only one ten thousand.
b) There are only one two thousand.
c) There are only three ten thousand.
d) There are only seven ten thousand.
e) There are only nine ten thousand.
What is rounding off?Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.
Given that;
Numbers are,
(a) 10650
(b) 21540
(C) 36907
(d) 74215
(e) 99999
Now, Numbers of ten thousand are,
(a) 10650
= 10000 + 650
Hence, There are only one ten thousand.
(b) 21540
= 10000 + 10000 + 1540
Hence, There are only two ten thousand.
(C) 36907
= 10000 + 10000 + 10000 + 6907
Hence, There are only three ten thousand.
(d) 74215
= 10000 + 10000 + 10000 + 10000 + 10000 + 10000 + 10000 + 4215
Hence, There are only seven ten thousand.
(e) 99999
= 10000 + 10000 + 10000 + 10000 + 10000 + 10000 + 10000 + 10000 + 10000 +9999
Hence, There are only nine ten thousand.
Learn more about the rounding number visit:
brainly.com/question/27207159
#SPJ2
Đặc tính nào sau đây KHÔNG PHẢI là đặc điểm của pháp luật:
a. Tính xã hội
b. Tính nhà nước
c. Tính giai cấp
d. Tính dân chủ
Answers
Please explain in english
Not looking for answer but does anyone know this specific topic in math
Answers
Answer:
This is called system of equations.
Step-by-step explanation:
This combines two equations and then lines them up to a system.
Answer:
Step-by-step explanation:
matrix
or
vector geometry
Identify the perimeter of the figure.
Answers
Answer:
20 + 7 + 10 + 26 + 24 + 12 + 16 + 7 = 122cm
Given:
.
• ON is tangent to Circle L at point N
ON= 6
• OQ = 3
O
6
N
3
Q
L
P
Find the length of PQ
Answers
Answer:
9
Step-by-step explanation:
By joining N to L, you will have a right angled triangle which is right angle at N. Then r^2+36=(3+x)^2. r=9/2. PQ=2r=9
Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Ariana will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Ariana's songs were played. Define the variables that you use to write the system.
Answers
Answer:
Commercials x = 7
Movies y = 2
Step-by-step explanation:
Let commercials = x
Let's movies = y
$40 is for commercials
$110 is for movies.
Commercials plus movies for the Year = 9
She earned total of $500
X+ y = 9..... equation 1
40x + 110y = 500.... Equation 2
Multipling equation one by 40
40x + 40y = 360
Subtracting equation one from equation 2
70y = 140
Y = 2
If y = 2
X + y = 9
X + 2 = 9
X = 9-2
X = 7
