Use the Squeeze Theorem to show that [tex]\lim_{t \to \infty} \frac{cos5t}{5t}[/tex]
Complete the following argument: for t arbitrary large and positive.

Im not sure how to break this problem down using the Squeeze Theorem, could anyone help?

Answers

Answer 1

Recall that [tex]\cos x[/tex] is bounded between -1 and 1 for all real [tex]x[/tex], so that

[tex]-1\le \cos(5t)\le 1[/tex]

[tex]\implies-\dfrac1{5t}\le\dfrac{\cos(5t)}{5t}\le\dfrac1{5t}[/tex]

Now take the limit of each side of the inequality:

[tex]\displaystyle\lim_{t\to\infty}\left(-\dfrac1{5t}\right)\le\lim_{t\to\infty}\dfrac{\cos(5t)}{5t}\le\lim_{t\to\infty}\dfrac1{5t}[/tex]

The bounding limits are both 0, so by the squeeze theorem the desired limit is also 0.


Related Questions

I need to find the measurement of AEB please help me!

Answers

Triangle BEC is an isosceles triangle.

The angles opposite the congruent sides are equal

x = measure of missing angle

180 = 54 + 2x

Subtract 54 from both sides

126 = 2x

Divide both sides by 2

63 = x

angle EBC and angle C = 63 degrees

Angle EBC and angle EBA are supplementary.

This means they add up to 180 degrees

180 = 63 + EBA

Subtract 63 from both sides

117 = EBA

the measure of a triangle = 180

Therefore,

The measure of angle AEB = 180 - (40 + 117) = 23 degrees

Answer:

104

Step-by-step explanation:

Kira bought 6 bags of popcorn for 15.36 how much would he pay for 4 bags

Answers

11.36 would be the answer

simplify 4-8÷2+3

please help

Answers

Answer:

4-8÷2+3=3

Step-by-step explanation:

Divide the numbers: 8/2=4

return to the problem: 4-4+3=3

Answer: 3

Answer:

it is 1

Step-by-step explanation:

because 4-8=-4\2=-2+3=1

please help me with math

Answers

Answer:

Given: P.E=6.0J Height (h)= 3m g=9.8m/s^2

mass=?

Formula: P.E=mgh

m=P.E/gh

Application: To find mass of an apple

Answer+unit= 0.2 kg

Step-by-step explanation:

m=P.E/gh

= 6kgm^2/s^2 ÷ 9.8m/s^2*3m

=0.2kg

If you decide to study 4 hours more a week during your junior year (32 weeks) with the expectation of getting $2,000 scholarship to college how much is your study time worth per hour

Answers

Answer: You will get $2,000 for 128 hour, or 2,000/128 = $15.625 per hour study time.

Step-by-step explanation:

We will give the solution of the following problem:

"If you decided to study for four hours a week during your junior year (32 weeks) with the expectation of getting a $2,000 scholarship to college, how much is your study time worth per hour?"

In 32 weeks you will have total of 4*32 = 128 study hours.

You will get $2,000 for 128 hour, or 2,000/128 = $15.625 per hour study time.

what is the value of x in the equation as a fraction 2(5x+4)=17

Answers

Answer:

x= 9/10

Step-by-step explanation:

2(5x+4)=17

Distribute

10x +8 = 17

Subtract 8 from each side

10x+8-8=17-8

10x = 9

Divid by 10

10x/10 = 9/10

x= 9/10

Divide both sides by 2:

5x + 4 = 8.5

Subtract both sides by 4:

5x = 8.5 - 4 = 4.5

Divide both sides by 5:

x = 4.5 / 5 = 0.9  or  9/10

Evaluate: 64 ^1/3

A) 3
B) 4
C) 6
D) 8

Answers

Answer:

(B) 4

Step-by-step explanation:

[tex]64 ^\frac{1}{3} \\\\\mathrm{Factor\:the\:number:\:}\:64=4^3\\\\=\left(4^3\right)^{\frac{1}{3}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\\\left(4^3\right)^{\frac{1}{3}}=4^{3\times\frac{1}{3}}\\\\3\times\frac{1}{3}=1\\\\=4^1\\\\=4[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\bf{(64)^ {\dfrac{1}{3}}}[/tex]

[tex]= \bf{\sqrt[3]{64^1} }[/tex]

[tex]\bf{\sqrt{64^1} \ \rightarrow 64}[/tex]

[tex]\sqrt[3]{64}[/tex]

[tex]\sqrt{64}= 8[/tex]

[tex]\bf{We\ solve\ half\ of\ 8 \ by\ dividing\ 8\ from\ 2 \ like: \dfrac{8}{2}}[/tex]

[tex]\bf{\dfrac{8\div2}{2\div2} = \dfrac{4}{1} = 4 }[/tex]

[tex]\bf{Thus, \ your\ answer\ is: \boxed{\bf{B. \ 4}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Subtract -3 – (-7). who will be first to answer....

Answers

Answer:

Its 4

Step-by-step explanation:

Because it is

Answer:

4

Step-by-step explanation:

1) First, distribute the negative sign to the -7. Because of this, the -7 will become a positive 7.

Equation: -3+7

2) Next, whenever there are two different signs, we are supposed to subtract the bigger number (7) with the smaller number (3).

Equation: 7-3=4

3) Finally, assign the greatest number sign. in this case, 7 is the greater number, and the 7 is a positive number; therefore, it will be a positive 4.

Hope this helps!

solve this question

Answers

Answer: a=56/15

Step-by-step explanation:

For this problems, it is important ot know how to read ratios. They can be read as fractions. Knowing this, we would use proportions to solve.

[tex]\frac{3a}{7} =\frac{8}{5}[/tex]                      [cross multiply]

[tex]15a=56[/tex]                  [divide both sides by 15]

[tex]a=\frac{56}{15}[/tex]

Now, we know that a=56/15.

Answer:

3 11/15

Step-by-step explanation:

3a : 7 : : 8 : 5

= 3a/7 = 8/5

=15a = 56

= 56/15 = 3 11/15

Move the horizontal and vertical sliders some more to stretch the image of the triangle. As you move the
sliders, observe what happens to the interior angles of each triangle. Based on your observations, can you say
that stretches preserve angle measurements?

Answers

Answer:

No, stretches do not preserve angle measurements. A stretch in either the horizontal or the vertical direction changes the interior angles.

Step-by-step explanation:

PLATO

Mark me brainliest plz :))

Answer:

No, stretches do not preserve angle measurements. A stretch in either the horizontal or the vertical direction changes the interior angles.

Step-by-step explanation:

cual es el valor absoluto de -|-42|​

Answers

Answer:

-42

Step-by-step explanation:

Scenario:You are a Geographic Information System (GIS) specialist who normally works at the Public Works Planning office.You are directed to report to the Incident Command Post (ICP) and have been assigned to the Planning Section Chief and will report to the Chief.You will be producing maps to display potential flooding impacts in the city and county.What NIMS Management Characteristics are you supporting? Select the two characteristics that apply.a. Integrated Communicationsb. Establishment and Transfer of Commandc. Chain of Command and Unity of Commandd. Accountabilitye. Dispatch/Deploymentf. Information and Intelligence Management

Answers

Answer: Chain of Command and Unity of Command ; Information and Intelligence Management

Step-by-step explanation:

Chain of Command typically loooks into an organization's hierarchical structure while unity of commands simply has to do with the reporting to ones designated supervisor.

Also, because maps are being produced, there'll be with the gathering, assessing, analyzing, sharing, and managing intelligence.

Therefore, the NIMS Management Characteristics that'll be supported are Chain of Command and Unity of Command ; Information and Intelligence Management.

The NIMS management characteristics that are mostly supported are:

A chain of Command is a unity of command.information and intelligence management.

The chain of command and unity of command is an overall hierarchy of the orpganization, while the unity of command says that the entire chain is always reporting to the similarly designated supervisor.

The information and intelligent management help the owner to take according to decisions forward premises of the information system.

As per the GIS when the maps have the process for the information would be gathering the information, assessing it, analyzing it, sharing the information to the delegated conducting the field, and then managing the intelligence of the information.

Thus, the NIS characteristics are chain and unity of command, and information and intelligence management.

To know more about geographic information system, refer to the link:

https://brainly.com/question/7551618

All right angles are congruent. Converse Inverse: Contrapositive

Answers

Answer:

No not all right angles are congruent.

Step-by-step explanation:

Jayden has 3/4 of a bag of dog food. his dog eats 1/10 of a bag per week. how many weeks will the dog food last. plzzzz send help I'm already failing

Answers

Answer: 7.5 weeks


Explanation:

Brainliest please

Need help with som math

Answers

Answer:

60

Step-by-step explanation:

3(3)²-2³-2³-5

81-8-8-5

81-16-5

81-21

60

your answer would be sixty

Ben drank 1/5 pitcher of lemonade. Tonya drank 1/2 of the lemonade. How much lemonade did they drink together?

Answers

Answer:

7/10ths of the picture has been digested.

Step-by-step explanation:

Let's divide this into tenths.

One fifth out of ten is equal to two, since 10/5 = 2. A half of ten is five, because 10/2 = 5. Adding five and two together gives us 7/10ths, which can not be reduced to a smaller amount.

Convert 4/6 to a decimal. (Round to the hundredths place)

Answers

Answer:

_

0.6

please give brainlist

hope this helped

Avas credit card balance is $64 if she makes a $25 payment then charges $79 find the balance of the card.

Answers

Answer:

6000 - 2500 = 3500

Ahora 3500 - 500 = 3000

ENTONSES la respuesta es 3000

Step-by-step explanation:

Put these numbers in order from least to greatest.
-36/40 , 3/5 , -12/24 , 1.

Answers

-36/40, -12/24, 1, 3/5


Given the function f(x) = -5|x + 1|
+ 3, for what values of x is f(x) = -12?

Answers

Answer:

2 and -4

Step-by-step explanation:

-5|x + 1| + 3 = -12

-5|x + 1| = -15

|x + 1| = 3

x + 1 = 3    /      x + 1 = -3

x₁ = 2        /      x₂ = -4

LaVilla is a village in the Italian Alps. Given its enormous popularity among Swiss, German, Austrian, and Italian skiers, all of its beds are always booked in the winter season, and there are, on average, 1465 skiers in the village. On average, skiers stay in LaVilla for 11 days. How many new skiers are arriving - on average - in LaVilla every day

Answers

Answer:

There are approximately 133 new skiers arriving every day

Step-by-step explanation:

Total number of skiers = 1465

time of stay for skiers = 11 days

How many new skiers are arriving on average = ???

To keep the average number of skiers available at each time constant, the number of skiers coming in and going out are fairly constant, and this is gotten by using the flow rate formula.

flow rate = amount available  ÷ flow time

flow rate = 1465 ÷ 11

flow rate = 133.18

flow rate = 133

∴ There are approximately 133 new skiers arriving every day

Which expression is equivalent to 5/6 / 7

Answers

Answer:

can you help me/

Step-by-step explanation:

What are the minimum and maximum values of x, for which x3 + x2 – 6x ≥ 0? minimum = –3, maximum = 0 minimum = 0, maximum = 2 minimum = –3, no maximum minimum = 2, no maximum Please answer quickly

Answers

Answer: Option C.

Step-by-step explanation:

The given inequality is

[tex]x^3+x^2-6x\geq 0[/tex]

Taking x common, we get

[tex]x(x^2+x-6)\geq 0[/tex]

Splitting the middle term, we get

[tex]x(x^2+3x-2x-6)\geq 0[/tex]

[tex]x(x(x+3)-2(x+3))\geq 0[/tex]

[tex]x(x+3)(x-2)\geq 0[/tex]

Related equation is

[tex]x(x+3)(x-2)=0[/tex]

[tex]x=-3,0,2[/tex]

These three points divide the number line in 4 parts.

Interval       Sign of [tex]x(x+3)(x-2)\geq 0[/tex]      Statement

(-∞,-3)              [tex](-)(-)(-)=(-)[/tex]                           False      

(-3,0)              [tex](-)(+)(-)=(+)[/tex]                            True  

(0,2)              [tex](+)(+)(-)=(-)[/tex]                              False      

(2,∞)              [tex](+)(+)(+)=(+)[/tex]                              True  

So, the solution set is (-3,0) ∪ (2,∞).

Thus, minimum value is –3 and no maximum value.

Therefore, the correct option is C.

Answer:

minimum = –3, no maximum

Step-by-step explanation:

The other guy here was completely correct, but just in case it assures anyone's doubts:

solve: 5y – 3.5 = 10.5

Answers

Answer:2.8

Step-by-step explanation:add 3.5 to the 10.5 which equals 14 then you divide 5 by 14 to get the y alone and it equals 2.8

5y-3.5=10.5
+3.5 +3.5
5y=14
5y/5= y
14/5= 2.8
Y=2.8

What is 0.5x10^2??????????????????

Answers

Answer:

0.5 x 10^2 = 50

Step-by-step explanation:

Hope this helped

Brainliest?

A parachute is describing at rate of 28 feet per minute find the total change of altitude of the parachuter after 4 mins

Answers

A parachute is describing at rate of 28 feet per minute find the total change of altitude of the parachuter after 4 mins.

112 feet

10 is 8% of a, and 5 is 4% of b. c equals b/a. What is the value of c?

Answers

Answer:

21

Step-by-step explanation:

A = 125
B = 125

B/A = 125/125
B/A= 1

C = 1

Please please please do all questions in the photo will give brainlest

Answers

1.) 403.97
2.)36
3.)8

1.)20
2.) 5/14
3.) 15.6

Answer: 1.    

               2. = 12

        3 on the left        = 8

         3 on the right     = 15

        1 on the right      =  20

         2 on the right     =   21/98

Step-by-step explanation:

Myra spends $5.70 a day on food and drink during the school year She skips the weekends . How much does she spend for the week?

Answers

Answer:

57$

Step-by-step explanation:

5.70 x 2 for both food and drink

the do 11.4 (the answer for the 1st step) x 5 for the week days giving you the answer of 57$

Answer:

$57 dollars

Step-by-step explanation                                                                                           Don't have one but i took the test and got it right

1/2 - 1/8

Answers should be in format 5/2 or 2/5. No decimals or mixed numbers

Answers

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

[tex]1/2 - 1/8\\\frac{1}{2}-\frac{1}{8}\\\\\mathrm{Least\:Common\:Multiplier\:of\:}2,\:8:\quad 8\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\frac{1}{2}=\frac{1\times\:4}{2\times\:4}=\frac{4}{8}\\\\=\frac{4}{8}-\frac{1}{8}\\\\=\frac{4-1}{8}\\\\=\frac{3}{8}[/tex]

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