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
Rectangles always have congruent diagonals.
False
True
False
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X increased by 10 is equal to 42
Answers
Answer:
x = 32
Step-by-step explanation:
x + 10 = 42, then you subtract 10 from both sides to get 32
2/5 of 16= (estimate each product)
Answers
Answer:
6.4 rounds down to 6.
Step-by-step explanation:
Divide 16 by 5. Multiply that number by 2.
What is the approximate area of the shaded region in the given square containing 2 semicircles? (Use * 3.14.) 10 cm 0 21.5 square centimeters O 50 square centimeters O 78.5 square centimeters O 100 square centimeters
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Answer:
yes
Step-by-step explanation:
bcuz
Answer:
Subtract the circle from the square
Step-by-step explanation:
(10× 10) - 25pi
In ΔVWX, w = 680 cm, ∠X=80° and ∠V=32°. Find the area of ΔVWX, to the nearest 10th of a square centimeter
Answers
Answer:
56
Step-by-step explanation:
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The area of the triangle.
= 1/2 x base x height
The area of the triangle is 105760 cm².
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In ΔVWX.
w = 680 cm
∠X=80°
∠V=32°
This means,
∠W + ∠X + ∠V = 180
∠W = 180 - 112
∠W = 68°
This means,
68° = 680
1° = 10
Now,
∠X=80°
x = 800 cm
∠V=32°
v = 320 cm
Now,
V
/ | \
(x) / | \ (w)
/ | \
W M X
(v)
680² = VM² + (320/2)²
462400 = VM² + 25600
VM² = 436800
VM = 661 cm
Thus,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 320 x 661
= 160 x 661
= 105760 cm²
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ2
What value of k makes the equation below true 33k=1,716
Answers
Answer:
Given:
33k=1,716
k=1716/33
k=52
PLEASE!! trigonometry
A= 61 degrees a=5 cm b=12 cm
Answers
Answer:
problem is undefined meaning there is no triangle
Don't we just love geometry! Speaking of that, I need some help!
Please only answer if you know the answer, the comment section is right below. Please don't waste my points!
Also, please show all of your work, you are trying to help me better understand the concept, not just give me the answer.
The image is down below. Show work! Thanks!
Answers
Answer:
23.3 milesStep-by-step explanation:
Use the law of sines:
a / sin A = b / sin B = c / sin CApply to the given triangle:
AC / sin 39 = 32 / sin 60AC / 0.629 = 32 / 0.866AC = 0.6293*32/0.866AC = 23.3 (rounded)WILL MARK BRAINLEST
You want to estimate how many fish there are in a pond. Suppose you cature 145 fish, tag them, and throw them back into the pond. After a couple of days, you go back to the pond and capture 580 fish, of which 29 are tagged.
An estimate for the number of fish in the pond is
fish
Answers
Answer:
450fish estimate
Step-by-step explanation:
A baker is experimenting with a new brand of yeast. He bakes his first batch of bread using the old brand of yeast that he usually uses and a second batch using the new brand of yeast. After baking both batches of bread, he compares the height, texture, and taste of each batch.
Answers
Answer:
control group: second batch
explanatory variable: new brand of yeast
response variable: height, texture, and taste
Step-by-step explanation:
Answer:
Explanatory variable = new brand of yeast
Response variable = height, texture, and taste
Control group = first batch
**See screenshot of graded answer
Each triangle in the net below has a base of 6 centimeters and a height of 8 centimeters. What is the surface area, in square centimeters, of the figure represented by the net? helpppppp i need help pls
Answers
The area of a triangle is 1/2 x base x height.
The area of the triangle is 1/2 x 6 x 8 = 24 square cm.
There are 4 identical triangles so 24 x 4 = 96 square cm.
The area of the square base = 6 x 6 = 36 square cm.
Total area = 96 + 36 = 132 square cm.
I WILL GIVE YOU 100 points and Braine at Math Properties of Equality, Part 2
For each expression, write an equivalent expression to show the
mathematical properties of equality.
Distributive Property:
6(m +4) = ?
Associative Property:
2 + (m + x) = ?
Commutative Property:
x + 3 = ?
Distributive Property:
3(2y - 6) = ?
Distributive Property:
m(y + 5) = ?
Answers
Answer:
1. 6(m + 4) = 6m + 24
2. 2 + (m + x) = (2 + m) + x
3. x + 3 = 3 + x
4. 3(2y - 6) = 6y - 18
5. m(y + 5) = my +5m
Step-by-step explanation:
1. Distributive property "distributes"/multiplies the 6 outside the parentheses to each term inside the parentheses.
2. Associative property deals with how terms and numbers are grouped into parentheses. The terms/numbers stay in the same order.
3. The commutative property means terms can change in order, and you will still get the same result.
4, 5. See #1 above. Distribute/multiply the number/term outside the parentheses to the numbers/terms inside.
Let me know if you have questions.
A car travels 30 – miles in
304
of an hour. What is the average speed, in miles per hour,
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Answers
Answer:
45.3 miles/h
Hope this will help you
Step-by-step explanation:
welcome
20 letters
5th grade math. Correct answer will be marked brainliest.
Answers
find the measure of angle P
Answers
Answer:
i dont see the picture clearly
Step-by-step explanation:
Enter an algebraic expression for the word expression.
The quotient of -5 and y
The expression is
Answers
9514 1404 393
Answer:
-5/y
Step-by-step explanation:
The wording "the quotient of A and B" is used to signify A/B.
Here, we want the quotient of -5 and y:
-5/y
Need help asap
Question 6
Answers
Answer:
AC=30
BD=30
BE=15
AB=27
Answer:
AC = 30, BD = 30, BE = 15, AB = 27, BC = 13.1
Step-by-step explanation:
AC = AE * 2
BD = BE * 2
BE = AE
AB = CD
BC = [tex]\sqrt{30^{2}-27^{2} }[/tex] (Pythagorean theorem)
Which function is best represented by this graph?
Answers
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
the -2 in the answer is the y intercept. 1/4 is the slop. rise over run, so up one and over four
Zander found these coins in his Couch
Answers
Answer:
91 cents
Step-by-step explanation:
3 quarters+3 nickel+1 penny=91 cents
Answer:
91 cents
Step-by-step explanation:
3 quarters=75c
3 nickels=15c
1 penny=1c
75c+15c+1c=91 cents
Someone help I don’t understand
Answers
Answer:
2052
Step-by-step explanation:
19 times 18=342
342 times 6=2052
Justin is going to invest $31,000 and leave it in an account for 7 years.
Assuming the interest is compounded quarterly, what interest rate, to the
nearest tenth of a percent, would be required in order for Justin to end up
with $45,000?
Answers
Answer:
5.4 percent
Step-by-step explanation:
an aquarium has 4 plants for every 3 fish there are 36 pants in the aquarium. How many fish are there?
A. 27 C. 32
B 48 D. 42
Answers
Answer:
A. 27 fish
Step-by-step explanation:
4/3 = 36/f
4f = 108
f = 27
Q8 Change 12 g to kilograms,
Answers
Answer:
0,012
Step-by-step explanation:
12 grams is 0.012 kilograms.
Hope this helps; have a great day!
40 points! Please help me
Answers
Answer:
x = 8
y = 14
Step-by-step explanation:
2x + 6 = 4x - 10 (Corresponding angles so they're equal)
2x - 4x = -10 - 6
-2x = -16
x = 8
2x + 6 + 13y - 24 = 180 (Supplementary angles so they add up to 180)
2(8) + 6 + 13y - 24 = 180
16 + 6 + 13y - 24 = 180
13y - 2 = 180
13y = 182
y = 14
Answer:
2x+6=4x-10[corresponding angle]
16=2x
x=8
again
2×8+6+13y-24=180°[linear pair]
13y=180+2
y=182/13
y=14
What is 1+1 I need help
Answers
Answer:
2
Step-by-step explanation:
1 + 1 = 2
Number Order: 1 2 3 4 5 6...
1 plus an additional value of 1 gives us the next number which is 2
What is the answer to 0=V+19
Answers
Answer:
v= -19
Step-by-step explanation:
Solve for V by simplifying both sides of the equation, then isolating the variable.
Answer:
-19
Step-by-step explanation:
+19 -19 = 0
Therefore,
V = -19
Subtract 19 from both sides 0 - 19 = -19,
-19 = V
2[tex]\sqrt{64[/tex]
Answers
Divide. Write your answer in simplest form. 9/2 / 1/4
Answers
Answer:
18
Step-by-step explanation:
9/2 / 1/4
keep 9/2
Change the operation to multiplication
flip 1/4 into 4 or 4/1
multiply on top and bottom and get 36/2
which 36/2 is 18 and 18 is the answer
Brainliest?
What are the solutions of x2 - 7x + 13 = 0 ? Imaginary numbers
Answers
Answer:
Step-by-step explanation:
I know what your thinking YOU DIDNT ANSWER!!!!! but think again i did, it is just an imaginary answer. dad jokeCRINGE!!!!!
Answer:
2 imaginary numbers
Step-by-step explanation:
x^2-7x+13=0
C=(-7)^2-4x1x13
D=-3
2 imaginary numbers
Juice is on sale with the rule "buy one, get one half-off.” Write an expression two different ways to represent the cost of buying two containers of juice, j, on sale. Enter the correct answers in the boxes.
Answers
Answer:
34
24
Step-by-step explanation:
divide 25 by 3