The limit of the given expression is
lim x -> infinity (x + sin(2x))/x = 1 + 0 = 1
To answer your question, L'Hopital's Rule is of no help in finding lim x -> infinity (x + sin(2x))/x because L'Hopital's Rule applies to indeterminate forms like 0/0 and ∞/∞.
In this case, as x approaches infinity, both the numerator and denominator approach infinity, making the expression an indeterminate form of ∞/∞. However, applying L'Hopital's Rule requires taking the derivative of both the numerator and the denominator, and since sin(2x) oscillates between -1 and 1, its derivative (2cos(2x)) will not help in finding the limit.
To find the limit using methods learned earlier in the semester, we can rewrite the given expression as:
lim x -> infinity (x + sin(2x))/x = lim x -> infinity (x/x + sin(2x)/x)
Now, let's evaluate the limit for each term separately:
lim x -> infinity (x/x) = lim x -> infinity 1 = 1 (since x/x always equals 1)
lim x -> infinity (sin(2x)/x) = 0 (since the sine function oscillates between -1 and 1, its value divided by an increasingly large x will approach 0)
So, the limit of the given expression is:
lim x -> infinity (x + sin(2x))/x = 1 + 0 = 1
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Gambarlah sebuah lingkaran dengan jari jari 2,5 cm. Lalu gambarlah 3 buah sudut keliling yg menghadap busur yang sama
Step-by-step explanation:
isidhxibdofeixeosgzifisvsoshzibdihddgd
Do you know anything about y=mx+b
Answer:
yes
Step-by-step explanation:
your m is your slope,your b is the y-intercept, and your y is what you are solving for.
Answer:
Y=mx+b is an equation for a linear equation
M is the slope of the line and B is the y-intercept
The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Every straight line can be represented by an equation: y = mx + b.
Hope this helps :))
Martha spent $12.35 at the local farmer's market. She bought 3 bundles of collards and paid $4.30 for some fruit. How much did each bundle of collards cost?
Answer:
12.35-4.30=8.05
8.05÷3= 2.68333333333333....
≈2.68
Proving trapezoid theorems Geometry
Answer:
ΔABD ≅ ΔACD by SAS, therefore;
[tex]\overline {BD} \cong \overline {CA}[/tex] by CPCTC
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
ABCD is a trapezoid [tex]{}[/tex] Given
[tex]\overline {BA} \cong \overline {CD}[/tex] [tex]{}[/tex] Given
[tex]\overline {BC} \parallel \overline {AD}[/tex] [tex]{}[/tex] Definition of a trapezoid
ABCD is an isosceles trapezoid [tex]{}[/tex] Left and right leg are equal
∠BAD ≅ ∠CDA [tex]{}[/tex] Base angle of an isosceles trapezoid are congruent
[tex]\overline {AD} \cong \overline {AD}[/tex] [tex]{}[/tex] Reflexive property
ΔABD ≅ ΔACD [tex]{}[/tex] By SAS rule of congruency
[tex]\overline {BD} \cong \overline {CA}[/tex] [tex]{}[/tex] CPCTC
CPCTC; Congruent Parts of Congruent Triangles are Congruent
SAS; Side Angle Side rule of congruency
Answer:
Step-by-step explanation:
just did it
Is this a, b, c, or d?
Answer:
Alright so let's start by elimination.
Step-by-step explanation:
It cannot be 1/4 (unless it's y or x)
Cannot be 1/2 unless it's the bottom part.
So that leaves you with 1/3 and 1/6, 1/6 is to small so it has to be 1/3.
Hope this helps!
Combine the like terms to create an equivalent expression:2r+1+(−4r)+7
Answer:
2r+1+(-4r)+7
= -2r+8
= -2(r+4)
Step-by-step explanation:
Work out
51.43% of 377.59cm
Give your answer founded to 2 DP
Answer:
194.194537 centimeters
Step-by-step explanation:
Answer:
194.19cm
Step-by-step explanation:
yeah yeah yeah yeah
I don’t know if this is correct !!!!! Please help answer correctly !!!!!!!!! Will mark Brianliest !!!!!!!!!!!
Answer:
change up to down the rest is right
Step-by-step explanation:
hope I helped!!
A rental car company offers a rental package for a mid-size car. The cost is comprised of a fixed \$ 40$40 administrative fee for the cleaning and maintenance of the car plus a rental cost of \$ 45$45 per day. Using xx for the number of days and yy for the total cost in dollars, construct a linear function to model the relationship between the number of days and the total cost of renting a mid-size car.
Answer:
y = 40 + 45x
Step-by-step explanation:
Fixed administrative fee for the cleaning and maintenance of the car = $40
rental cost = $45 per day
x = number of days
y = total cost in dollars
y = 40 + 45x
This shows the relationship between the number of days and the total cost of renting a mid-size car.
5+5-66564+6367347646-4848
Answer:
6367276244 6367276244
6367276244 6367276244
Answer:
6367276244
Step-by-step explanation:
In circle O, AC and BE are diameters. The measure of arc DC is 50°. What is the measure of EBC?
Answer:
The angle measure would be 40°
Step-by-step explanation:
Right angles have a measure of 90. Since DC is 50, 90-50 is 40.
The angle measure of ∠EBC would be 40°.
What is arc?The arc is a portion of the circumference of a circle
Right angles have a measure of 90°.
∵∠BOD=90°
Since ∠DC is 50°,
∠EBC = ∠BOD-∠DC
∠EBC = 90°-50° is 40°.
The angle measure of ∠EBC would be 40°.
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Find the measure of each angle in the angle pair described.
The measure of one angle is twice the measure of its supplement. What are the measures of the two angles?
Answer:
The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree
Two siblings' ages have a sum of 64 years. The older sibling was born 6 years before their young sibling.
Write a system of 2 equations. Solve the system using substitution. Report your answer in the form of (older, younger).
Hi!
So we have to make a system of equations here.
Let sibling 1 be O and sibling 2 be Y (for older and younger)
So:
O + Y = 64
O = 64 - Y
(Either one works)
The older sibling is 6 years older.
O = Y + 6
Make everything in terms of Y.
64 - Y = Y + 6
Same to both:
58 = 2y
2y = 58
Divide by 2 on both sides:
y = 29
Since the older sibling is 6 years older:
29 + 6 = 35
Y = 29
O = 35
Let me know if you have any questions.
You can upgrade lighting at your factory to LED bulbs that coast 6.95 each and last an average of 5 years.
Answer:
$200
Step-by-step explanation:
Here is the full question
You can upgrade lighting at your factory to LED bulbs that cost $6.95 each and last an average of 5 years. It costs $3 in labor to change a bulb. Over a 10-year period, about how much will it cost per year to install LED bulbs in 100 lamps and change the bulbs when they burn out?
in 10 years, the bulbs would be changed twice
Total cost incurred per bulb in 10 years = (6.95 + $3) x 2 = $19.90
Since there are 100 bulbs, total cost incurred would be - $19.90 x 100 = $1990
Cost per year = $1990 / (6.95 + $3) = $200
help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
did the math for it!!
B, jake.
loooooooooooooooooll
holly has 368 pet pal cards Dara has 243 cards how much more does holly have then Dara
Answer:
125
Step-by-step explanation:
Answer:
125
Step-by-step explanation:
368 - 243 = 125
STATE 2 DECIMALS BETWEEN 2.10 AND 2.11 Please help!
Answer:
There are many decimals between 2.10 and 2.11.
Examples:
2.101, 2.102, 2.103, 2.104, 2.105, 2.106, 2.107, 2.108, 2.109
You can choose 2 from these examples.
Helpppppppp pls help .
Answer: X= 1 2 3 4 Y= 5 8 11 14
Step-by-step explanation: i tried my best
The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NOLM:MN:NO is equal to 3:1:2.3:1:2. If LO=30,LO=30, find LN.LN.
Answer:
[tex]|LN| = 24[/tex]
Step-by-step explanation:
Given
[tex]LM:MN:NO = 3:1:2[/tex]
[tex]LO = 30[/tex]
Required
Find LN
[tex]LN = LM + MN[/tex]
From the ratio, LM = 3 and MN = 1
So:
[tex]LN = 3 + 1[/tex]
[tex]LN = 4[/tex]
LN and NO can be represented as:
[tex]LN : NO = 4 : 1[/tex]
The length of LN is then calculated as:
[tex]|LN| = \frac{LN}{LN+NO}*|LO|[/tex]
[tex]|LN| = \frac{4}{4+1}*30[/tex]
[tex]|LN| = \frac{4}{5}*30[/tex]
[tex]|LN| = \frac{4*30}{5}[/tex]
[tex]|LN| = \frac{120}{5}[/tex]
[tex]|LN| = 24[/tex]
PLZ HELP!!! WILL GIVE HIGHEST POINTS IF THE ANSWER IS CORRECT!!!
Answer: -5 Hope this helps :)
Step-by-step explanation:
Brainlist Plz?
Every year Ethan ears 38,428. Every year he spends 21,728 on expenses. How much money should Ethan have leftover?
Answer:
16,700
Step-by-step explanation:
38,428
_
21,728
=
16,700
What is the y-intercept
Step-by-step explanation:
To find the y intercept we need to find slope first which can be done by taking 2 points and using the slope formula
5 - 10
---------- = -5/3
12--9
The slope is -5/3 now we take one point substitute the slope in and find the y intercept
5=-12( -5/3) +b
5= 20+ b
-15 =b
The y-intercept is -15
Rahul sold a painting at 10% profit. If he had sold it for 240 more, he would have made 15% profit. What is the C.P. of the painting?
please tell ans step by step..
Answer:
$4800
Step-by-step explanation:
Let x be the C.P of the painting.
Profit=10% of x
Profit=[tex]\frac{10}{100}\times x=\frac{10x}{100}[/tex]
If S.P increase by 240 then
Profit=15% of x=[tex]\frac{15x}{100}[/tex]
For first case
S.P=C.P+ Profit
S.P=x+10x/100
S.P=[tex]\frac{100x+10x}{100}=\frac{110}{100}x[/tex]
For second case
New S.P[tex]=x+\frac{15}{100}x[/tex]
=[tex]\frac{115}{100}x[/tex]
According to question
[tex]240+S.P=\frac{115}{100}x[/tex]
[tex]240+\frac{110x}{100}=\frac{115}{100}x[/tex]
[tex]240=\frac{115}{100}x-\frac{110x}{100}[/tex]
[tex]240=\frac{115x-110x}{100}[/tex]
[tex]240=\frac{5}{100}x[/tex]
[tex]x=\frac{240\times 100}{5}[/tex]
[tex]x=4800[/tex]
Hence, the C.P of the painting=$4800
Julie has $80,000 to invest. She invests part at 5%, one fourth this amount at 6%, and the balance 7%. Her total annual income from interest is $4,700. Find the amount invested at each rate.
Answer:
Julie invested $ 25,000 at 7%, $ 20,000 at 6%, and $ 35,000 at 5%.
Step-by-step explanation:
Given that Julie has $ 80,000 to invest, and she invests part at 5%, one fourth this amount at 6%, and the balance 7%, knowing that her total annual income from interest is $ 4,700, to find the amount invested at each rate se you must perform the following calculation:
80,000 / 4 = 20,000
20,000 x 0.06 = 1,200
4,700 - 1,200 = 3,500
60,000 x 0.07 + 0 x 0.05 = 4,200
50,000 x 0.07 + 10,000 x 0.05 = 4,000
40,000 x 0.07 + 20,000 x 0.05 = 3,800
30,000 x 0.07 + 20,000 x 0.05 = 3,600
25,000 x 0.07 + 35,000 x 0.05 = 3,500
Thus, Julie invested $ 25,000 at 7%, $ 20,000 at 6%, and $ 35,000 at 5%.
Jane made a poster that had a length of 1 2/3 feet and a width of 5/6 feet. What is the perimeter of her poster?
answers; 1 7/18, 2 1/2, 3 feet, and 5 feet.
Answer:
5 feet
Step-by-step explanation:
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket
Answer:
senior citizen tickets are $10 and child tickets are $8
Answer:
senior is 10 and child is 8
Step-by-step explanation:
3.5 m = ______cm
PLEASE HELP ME!!!!!!!
Answer:
Formula *10
Step-by-step explanation:
35
PLEASE HELP! WILL MARK BRAINLIEST IF U ANSWER CORRECTLY! IF WRONG U WONT GET IT
Answer:
1120 super easy
Step-by-step explanation:
8x10=80
80x14=1120
Let
cos
(
2
∘
)
≈
0.9994
What is the the value of
x
, in degrees, for
sin
(
x
)
≈
0.9994
?
Answer:
can write it again soon as you can do it again
survey of a company's employees explored the relationship between employee status and support of a new workplace safety policy The results are displayed in the following two-way frequency table. Workplace Safety Policy For Against Total Part-Time
Employee 20 60 80 Full-Time Employee 100 20 120 Total 120 BO 200 used on the table above, which of the following statements are true? There are twice as many part-time employees against the workplace safety policy than full-time employees against the workplace safety policy IL There are more employees for the workplace safety policy than against the workplace safety policy There is an equal number of part-time employees and full-time employees.
Answer:
ll and lll
Step-by-step explanation: