The limit as n approaches infinity of [(n^2 - 1)/(n^2 + 1)] is equal to 1. The limit as n approaches infinity of [(n - 1)/(n^2 + 1)] is equal to 0.
(a) The limit as n approaches infinity of [(n^2 - 1)/(n^2 + 1)] is equal to 1.
To see why, note that both the numerator and denominator approach infinity as n goes to infinity. Therefore, we can apply the limit law of rational functions, which states that the limit of a rational function is equal to the limit of its numerator divided by the limit of its denominator (provided the denominator does not approach zero). Applying this law yields:
lim(n→∞) [(n^2 - 1)/(n^2 + 1)] = lim(n→∞) [(n^2 - 1)] / lim(n→∞) [(n^2 + 1)] = ∞ / ∞ = 1.
(b) The limit as n approaches infinity of [(n - 1)/(n^2 + 1)] is equal to 0.
To see why, note that both the numerator and denominator approach infinity as n goes to infinity. However, the numerator grows more slowly than the denominator, since it is a linear function while the denominator is a quadratic function. Therefore, the fraction approaches zero as n approaches infinity. Formally:
lim(n→∞) [(n - 1)/(n^2 + 1)] = lim(n→∞) [n/(n^2 + 1) - 1/(n^2 + 1)] = 0 - 0 = 0.
(c) The limit as x approaches 2 of [x^4 - 2sin(xπ)] is equal to 16 - 2sin(2π).
To see why, note that both x^4 and 2sin(xπ) approach 16 and 0, respectively, as x approaches 2. Therefore, we can apply the limit law of algebraic functions, which states that the limit of a sum or product of functions is equal to the sum or product of their limits (provided each limit exists). Applying this law yields:
lim(x→2) [x^4 - 2sin(xπ)] = lim(x→2) x^4 - lim(x→2) 2sin(xπ) = 16 - 2sin(2π) = 16.
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Write a system of linear inequalities so the points,(1,2) and (4,-3) are solutions of the system, but the point (-2,8) is not a solution of the system.
Answer:
The sample system is:
y < 5y > x - 8see the attached
The points (1, 2) and (4, -3) are in the intersected region but the point (-2, 8) is outside
Write an explicit and recursive rule for the geometric sequence -5, 10, -20, 40… and use it to find the 12th
Answer:
See solutions below
Step-by-step explanation:
Given the sequence -5, 10, -20, 40...
The nth term of the GP is expressed as;
Tn = ar^n-1
a is the first term
r is the common ratio
n is the number of terms
From the sequence, a = -5
r = 10/-5 = -20/10 = -2
Substitute
Tn = -5(-2)^n-1
This gives the explicit formula
For recursive;
a1 = -5
a2 = 10 = -2(-5) = -2a1
a3 = -20 = -2(10) = -2a2
From the shown sequence, we can see that;
an = -2an-1
This gives the recursive formula
Get the 12th term;
Using the explicit formula
T12 = -5(-2)^12-1
T12 = -5(-2)^11
T12 = -5(-2048)
T12 = 10240
Hence the 12th term is 10240
the original pattern for dress is 33 3/4 inches long. kimmy needs her dress to be 32 1/2 inches long how much shorter than the pattern does kimmy need to make her dress
Answer: 1 1/4
Step-by-step explanation: 32 1/2 is the same as 32 2/4 so all you have to do is subtract 32 2/4 from 33 3/4 which leaves you with 1 1/4
in estimating the body temperature of a person, what difficulties did you encounter?Explain
Answer:
In general , While estimating a bodies temperature that temperature is not the same for long, the temperature of the body is not at homeostasis, the temperature constantly has bumps and drops in the temperature this causes in accuracy thats why the thermometer takes 10-20 seconds because it takes the average of all the temperature's so it is accurate, that is a difficulty when estimating temperature because estimates are not good and the temperature keeps having ups and downs.
Find the slope of the line
Answer:
-1
Step-by-step explanation:
Using rise over run for the two points
4 - 0/ -1 - 3 = -1
Answer:
We found 2 coordinates
1. ( 0 ,3)
2.(3,0)
Now slope = tan theta = 3/3 = 1
Answer is 1
Mark it as brainlist answer
Step-by-step explanation:
PLZZZZZ HELP ME!
It’s math btw
Answer:
1. 9/10
2. 15/16
4. 3/5
5. 3/5
Step-by-step explanation:
1. 7/10 + 2/10 = 9/10
2. 13/16 + 2/16 = 15/16
4. 7/15 + 2/15 = 9/15 = 3/5
5. 9/20 + 3/20 = 12/20 = 3/5
Answer: 1 r1 for second
Step-by-step explanation: 13/16+2/16=15/16 divide 15/16 gets 1 r1
The square table top has an area of 369 square
inches. The length of one side of the table top is
between which two measurements?
Answer:
19 in. and 20 in.
Step-by-step explanation:
18^2 = 18 * 18 = 324
19^2 = 19 * 19 = 361
20^2 = 20 * 20 = 400
369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.
Answer:
19 in. and 20 in.
Step-by-step explanation:
18^2 = 18 * 18 = 324
19^2 = 19 * 19 = 361
20^2 = 20 * 20 = 400
369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.
f(x)= 10x find the inverse of the function
find the value and add them together
Huey is reading a book that is 697 pages long.
He tells a friend that he is about 3/4 of the way done.
About how many more pages must Huey read before he finishes the book?
Answer:
700 books huey finish he your answer
Answer:
175 pages
Step-by-step explanation:
Answer:
. 175
Step-by-step explanation:
There are 2 ways that we can find the answer to this question:
1. Take 1/4 of 697
2. Take 3/4 of 697 and minus the product from 697.
Let's do it both ways:
If we are doing it the first way it would look like this:
(1/4)(697) = 175
Note that we get 1/4 because Huey already read 3/4 of the book so he has 1/4 left.
The second way would look like this:
(3/4)(697) = 523
679 - 523 = 174 (roughly 175)
Therefore, the answer to your question would be . 175. pls mark brainliest
There are 20 animals in the barn. There are chickens and sheep in the barn. If there are
a total of 62 legs, how many of each animal are there? *
Answer: Nope I was wrong
Work out, giving your answer in its simplest form:
4/7 divided by 2 1 / 3
Step-by-step explanation:
4/7÷21/3
=4/7*3/21
=12/147
Answer:
[tex]\frac{12}{49}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{7}[/tex] ÷ 2 [tex]\frac{1}{3}[/tex] ← change mixed number to improper fraction
= [tex]\frac{4}{7}[/tex] ÷ [tex]\frac{7}{3}[/tex]
To perform the division
Leave the first fraction. change division to multiplication and turn the second fraction upside down.
= [tex]\frac{4}{7}[/tex] × [tex]\frac{3}{7}[/tex] ← multiply numerators/ denominators together
= [tex]\frac{4(3)}{7(7)}[/tex]
= [tex]\frac{12}{49}[/tex]
Factor completely
x^2 - 8x + 16
Answer:
(x - 4)^2
Step-by-step explanation:
PLEASE HELP 50 POINTS Which terms can be combined in the expression below? Select three options.
StartFraction 5 over 6 EndFraction a minus 2 b minus 16.3 + StartFraction b over 12 EndFraction + c minus 0.9 b
StartFraction 5 over 6 EndFraction a
–2b
–16.3
StartFraction b over 12 EndFraction
–0.9b
Answer:
it -16.3
Step-by-step explanation:
Answer:
Answer:
Option 2nd , 4th and 6th correct2,4 and 6
Step-by-step explanation:
Like terms are those terms which have same variable to the same power.
Combine like terms
Simplify:
Therefore, the term can be combined in the given expression is,
2, 4 and 6Barinliest?Cual es el 5% de 80?
Find the distance between (2, 8) and (−6, 2).
The distance is ( ) units.
Answer:
✓100 = 10
Step-by-step explanation:
2= x1
8= x2
-6= y1
2= y2
Then you apply your distance formula to solve.
Hope it helps
Write the equation of a line in slope intercept form.
(-3,-9 ) and (2,6)
Answer:
y = 3x
Step-by-step explanation:
I didn't mean to click an answer but please help me out
Answer:
135
Step-by-step explanation:
135+45=180, and supplementary angles always equal 180
Answer:
The answer is 135
Step-by-step explanation:
Definition of supplementary angles: either of two angles whose sum is 180°, so 180 - 45 = 135!
Please mark as brainliest.
How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?
Answer:
186.7 cubes
Step-by-step explanation:
How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?
Step 1
We find the volume of the box
= Length × Width × Height
Length = 3 1/3 inches = 10/3 inches
Width = 2 2/3 inches = 8/3 inches
Height = 2 1/3 inches = 7/3 inches
The volume of the box =
10/3 inches × 8/3 inches × 7/3 inches
= 560/9 cubic Inches
= 62 2/9 cubic inches
Step 2
How many 1/3 inch cubes would fill the box.
This is calculated as:= 62 2/9 cubic inches/ 1/3 inches
= 560/9 ÷ 1/3
= 560/9 × 3/1
= 186.66666667 cubes
Approximately = 186.7 cubes
Calculate the amount of work done if you use a 150N force to push a 50kg box 5m across the kitchen floor.
Answer:
750 J
Step-by-step explanation:
1. Um prêmio em dinheiro foi dividido entre 3
pessoas: a primeira recebeu 1/4 do valor do
prêmio a segunda recebeu 1/3 e a terceira
ganhou R$ 1000,00. Então, o valor desse prêmio,
em reais, era de:
a) 2400,00
b) 2200,00
c) 2100,00
d) 1800,00
what is 41x plus 21x
Find the maeasure of the exterior angle in the figure
Answer:
the answer would be 5b as the exterior angle is subdivided with the co efficient
Step-by-step explanation:
convert the decimal into a reduce fraction.
Answer:
hey i dont really know, but look up calculator soup, it has a ton of different calculators and may be able to help u
Step-by-step explanation:
/
I dont really understand this question, can anyone help me out?
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Angles.
Complementary angles sum up together to become 90°.
Supplementary Angles sum up together to become 180°.
hence,
1.) Ans ==>Angle ABC and Angle NMP
2.) Ans ==> angle ABC and angle EFG
Find the slope of the line passing through the points (-7, 4) & (-7, -8)
Answer:
Undefined
Step-by-step explanation:
The equation for finding the slope is:
y2 - y1
------------
x2 - x1
--------------------------------------------------------------------------------------------------------
4 - (-8)
----------
-7 - (-7)
-----------------------------------------------------------------------------------------------------------
4 + 8
--------
-7 +7
---------------------------------------------------------------------------------------------------------
12
----
0
---------------------------------------------------------------------------------------------------------
The slope is Undefined, so there is no answer
what iis the answer to this question
1/5x40
Answer:
8
Step-by-step explanation:
Answer:
1/5 x 40 = 8
(Hope this helps! Btw, I am the first to answer.)
Hello brainly people, can someone please explain how I do this? I really need help...
A object falls at 16t^2 feet in t seconds you drop a rock from a bridge that is 906 what is the hight in feet after the rock is droped
Answer:
824 feet
Step-by-step explanation:
Given
[tex]h(t) = 16t^2[/tex]
[tex]H = 906[/tex] -- Initial Height
Required
Calculate the height after 2 seconds --- missing from the question
First, we calculate the distance moved in 2 seconds
[tex]h(t) = 16t^2[/tex]
[tex]h(2) = 16*2^2[/tex]
[tex]h(2) = 16*4[/tex]
[tex]h(2) = 64[/tex]
This means that the object covered 64feet
The object current height is then calculated as:
[tex]Height = H - h(t)[/tex]
t = 2. So, the equation becomes
[tex]Height = H - h(2)[/tex]
Substitute values for H and h(2)
[tex]Height = 906- 64[/tex]
[tex]Height = 824[/tex]
Help me please!!!!!!
Answer:
(2,8)
Step-by-step explanation:
I'm not so sure but if I were answering I would have picked (2,8)
someone help me with this answer please !!
Answer:
-27
Step-by-step explanation: