Determine whether the sequence converges or diverges. If it converges, find the limit. [Hint:
consider limit laws, the Squeeze Theorem, behavior of related real-valued functions, etc.]
(a) an = 2 + (0.86)^n
(b) an =(4^n)/(1+9^n)
(c) an = arctan(ln n)
Answers
(a) converges; consider the function f(x) = a ˣ, which converges to 0 as x gets large for |a | < 1. Then the limit is 2.
(b) converges; we have
4ⁿ / (1 + 9ⁿ) = (4ⁿ/9ⁿ) / (1/9ⁿ + 9ⁿ/9ⁿ) = (4/9)ⁿ × 1/(1/9ⁿ + 1)
As n gets large, the exponential terms vanish; both (4/9)ⁿ → 0 and 1/9ⁿ → 0, so the limit is 1.
(c) converges; we know ln(n ) → ∞ and arctan(n ) → π/2 as n → ∞. So the limit is π/2.
Related Questions
What is the solution to the system of equations?
y = 2/3x + 3
x=-2.
Answers
Ruby is designing a t shirt logo for her company. The shirt printing company offers 12 colors to choose from for the logo
design. If any number of colors can be chosen, how many different color combinations are possible?
Answers
Answer: 4096
Step-by-step explanation: 2^12
There are 4096 different color combinations are possible.
What is the combination?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
Given that The shirt printing company offers 12 colors to choose from for the logo design.
Here, we need to get the possible number of color combinations possible.
Since any number of colors can be chosen, there are no restriction.
That means the number of possible color combinations are;
[tex]2^{12} = 4096[/tex]
There are 4096 different color combinations are possible.
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The formula for the circumference, C, of a circle with given radius, r, is C = 2πr. meters? what is the circumference of a circle with a radius of 3 1/2 meters? (use 22 as an estimate for it.)
A. 7 meters
B. 11 meters
C. 22 meters
D. 44 meters
Answers
Answer:
22
actual answer was 21.99
HELP ME PLSSSSSSSSSSS IF I FAIL I M Screwed
Answers
Answer:
41
Step-by-step explanation:
What is the prime factorization of 84?
A. 2•3•7
B. 3•4•7
C. 2•2•21
D. 2•2•3•7
Answers
Answer:
D. 2•2•3•7
Step-by-step explanation:
Si a y b son los catetos de un triángulo y c su hipotenusa determina el lado que falta a= 16,b=34*
Answers
Answer:
the aswer is b
Step-by-step explanation:
i
A company makes 150 bags.
23 of the bags have buttons but no zips.
35 of the bags have zips but no buttons.
49 of the bags have neither zips nor buttons.
How many bags have zips on them?
Answers
PLEASE HELP! WILL MARK BRAINLIEST!!
How did advancements in the steam engine affect industrialization? (5 points)
By eliminating the need for transportation of goods by ship
By decreasing the production time for textiles
By eliminating the need for a water source to power mills
By polluting crowded urban areas
Answers
Answer:
By decreasing the production time for textiles
Step-by-step explanation:
Find the missing side of this right triangle. [Pythagorean Theorem]
Answers
Answer: 12 x 7 = 72
Step-by-step explanation:
Answer:
Square root of 193
Step-by-step explanation:
7^2+12^2=x^2
Switch sides: x^2=7^2+12^2
After everything is squared: x^2=49+144
x^2=193 OR x=\sqrt{193}
Please help
See the picture
Answers
Answer:
6
Step-by-step explanation:
Gud luck
ТDaP is a booster shot that prevents Diphtheria, Tetanus, and Pertussis in adults and adolescents. It should be administered every 8 years in order for it to remain effective. A random sample of 500 people living in a town that experienced a pertussis outbreak this year were divided into two groups. Group 1 was made up of 132 individuals who had not had the TDaP booster in the past 8 years, and Group 2 consisted of 368 individuals who had. In Group 1, 15 individuals caught pertussis during the outbreak, and in Group 2, 11 individuals caught pertussis. Is there evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were? Test at the 0.05 level of significance.
Enter the test statistic - round to 4 decimal places.
Enter the P-Value - round to 4 decimal places.
Is there evidence to suggest the proportion of those who caught pertussis is higher for those who were not up to date on their booster?
Answers
Answer: 76.8356 and 12.5372
Step-by-step explanation:
Alexis is going to Vegas for the weekend! She decides to try her hand at a new game that Casino QuickCash is promoting. For this game, you pay $6 to play. A dealer shuffles and then randomly draws a card from a standard deck of 52 cards. If the card drawn is a diamond, Alexis wins nothing. If the card drawn is an even-numbered card (2,4,6,8, or 10) from the remaining three decks, Alexis wins $8. Otherwise, Alexis wins $12. a) Alexis's expected winnings per game is (rounded to the nearest cent):
Answers
Answer:
$10.46
Step-by-step explanation:
Amount that can be won by Alexis ( xi ) = $0, $8 , $12
probability ( pi )
P( $0 ) = 13 / 52 = 1 / 4
P( $8 ) = 15 / 39 ( given that she wins this when an even number is drawn from three remaining decks )
P ( $12 ) = 1 - 15/39 = 24 / 39
a) Alexis expected winnings per game
= ∑ xi * pi = ( 0 * 1/4 ) + ( 8 * 15/39 ) + ( 12 * 24 / 39 )
= $0 + ( 120 / 39 ) + ( 288 / 39 ) = $10.46
if (-1 ,5 ) satisfies the equation 3x + Ky =7 then k =?
Answers
Answer:
k = 2
Step-by-step explanation:
3(-1) + k(5) = 7
-3 + 5k = 7
5k = 10
k = 2
The value of K in the equation 3x + Ky =7 is 2.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Equation 3x + Ky =7.
And we have also given that (-1, 5) satisfies the equation.
That means,
(-1, 5) is a solution of the equation.
To find the value of K;
Substitute the value of x = -1 and y = 5
So,
3x + Ky =7,
3(-1) + K(5) =7
-3 + 5K = 7
5K = 10
K = 2
Therefore, the value of K is 2.
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Need help I will offer brainalist + 10 points for correct answer (:
Answers
The reason why it is not B as the other person answered is because supplementary makes 180 degrees. When that is not the correct answer to this question.
C is your answer! I hope that helped :)
In a survey of 526 visitors to the craft center, 378 want the craft center to be open later in the evenings. What is the interval that is likely to contain the true population proportion?
37% to 69%
16% to 17%
20% to 38%
0% to 53%
Answers
Answer:
37% to 69%
Step-by-step explanation:
Plz help if correct ill give brailiest
Answers
Answer:
At most 5
At least 0
Step-by-step explanation:
22 - 17 = 5
You can't have no more than 5, and you can have none join at all.
Answer:
At the most, it will be 5
At least it will be 0
You can't have anymore than 5, and you can have none join at all.
Step-by-step explanation:
22 - 17 = 5
You can't have anymore than 5, and you can have none meet at all.
Question 6 of 23
What is the slope-intercept equation of the line below?
Answers
Write 11/8 as a mixed fraction
Answers
Answer:
1 3/8
Step-by-step explanation:
Since 11 is over 8 that means you already have a whole number so you just add the 3 and you get 1 3/8
To check just in case you just multiply the whole number and denominator and then add the numerator.
What's greater? 18% or 11/55?
Answers
Answer:
11/55
Step-by-step explanation:
11/55 = 20%
18% = 18%
Answer:
11/55 is greater
Step-by-step explanation:
18% is less because divided by 100 it will be 0.18 and if you multiply 11/55 the answer is 0.20
Please give me an right answer and explain pleaseeee!!! And set up and equation before solving !
The difference between two numbers is 4. The sum of the smaller number and three times the larger number is 36. What are the two numbers?
Answers
Answer:
The two numbers are 6 and 10.
Step-by-step explanation:
First, you have to form equations. With the given informations, let x be the larger number and y be the smaller number, the equations will be :
x - y = 4
3x + y = 36
Next, you have to solve the simultaneous equations :
x - y = 4 ---------- (1)
3x + y = 36 ------- (2)
(2) + (1)
3x + y + x - y = 36 + 4
4x = 40
x = 10
Substitute x = 10 into (2)
3(10) + y = 36
30 + y = 36
y = 36 - 30
y = 6
Find the area of the rhombus. Each indicated distance is half the length of it’s respective diagonal.
(image included)
Answers
Answer:
384 ft²
Step-by-step explanation:
12x16x2=384
A water balloon was launched into the top of the hill 38 feet above the ground
Answers
Answer: -71.104 ft/sec
Step-by-step explanation:So you need to know how fast the balloon is moving when it hits this person's head. velocity is based on time. So you need the time that it hits this person's head. You can get time from the position equation. Because the balloon hits this person's head 6 feet from the ground, you know that the final position is at 6 so you plug that into the position equation and solve for t. You look and see what the appropriate t value is and plug it into the velocity equation and see what the answer is.
6=-16t^2+40t+60
0=-16t^2+40t+54
plug in those values into the quadratic formula or your calculator and you get:
t = -.972
or
t = 3.472
since you can't have negative time, the other answer must be it.
So you then plug it in and solve.
v(3.472) = -32(3.472) + 40
which is approximately -71.104 ft/sec
or if they just want speed, 71.104 ft/sec. (remember, speed is velocity without direction)
Can someone help please, please no dirty links you will be reported.
Answers
Answer:
3.25
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at which approximate rate in feet per minute did the plane climb to the cruising altitude of 35,000 feet
Answers
What rational number is equivalent to .36 repeating
Answers
Answer:
4/11
Step-by-step explanation:
i think,,,,try it and maybe its right
Simplify -3 p3 + 5 p + (-2 p2 ) + (-4) - 12 p + 5 - (-8 p3 ). Select the answer in descending powers of p . 1 - 7 p - 2 p2 + 5 p3 1 + 7 p + 2 p2 - 5 p3 5 p3 - 2 p2 - 7 p + 1 -5 p3 + 2 p2 + 7 p + 1
Answers
Step-by-step explanation:
Let's simplify step-by-step.
−3p3+5p−2p2−4−12p+5−−8p3
=−3p3+5p+−2p2+−4+−12p+5+8p3
Combine Like Terms:
=−3p3+5p+−2p2+−4+−12p+5+8p3
=(−3p3+8p3)+(−2p2)+(5p+−12p)+(−4+5)
=5p3+−2p2+−7p+1
Answer:
=5p3−2p2−7p+1
Need Help Geometry Question I will give brainliest
Answers
8 4 pairs of shoes cost $80. What is the cost of 7 pairs of shoes?
Answers
Answer: 140
Step-by-step explanation:
Uang Indonesia: Rp 1,155,600
Uang Amerika Serikat= $80
Uang Malaysia= $331.52
40% de_____=60
Es urgente por favor con explicación
Answers
Answer:
Hola 15 es tu respuesta
Step-by-step explanation:
por 40% puedes convertirlo en 4, multiplicar por 15 y obtendrás 60
espero que esto ayude
What is the area of the figure?
15in.
30in
-50in.
The area of the figure is
Answers
Answer:
2,250
Step-by-step explanation: