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Art [367]
3 years ago
15

Prove

le="\lim_{x \to 0} \frac{sin x}{x} = 1" alt="\lim_{x \to 0} \frac{sin x}{x} = 1" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
SpyIntel [72]3 years ago
3 0

Answer:

See below.

Step-by-step explanation:

sin x / x.

You can prove this by L'Hopitals Rule.

If x = 0 then the function = 0/0 so the above rule is applicable here.

Differentiating top and bottom we get cos x / 1  = cos x.

Limit x --> 0 of cos x = 1 so it is proved.

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One liter of paint covers 100 square feet. How many gallons of paint does it take to cover a room whose walls have an area of 80
mezya [45]
1 gallon is 3.78 L
100 sq feet needs 1 L
800 sq feet needs x

100/800 = 1/x
100x = 800
x = 800/100
x = 8 L

If you use the fact that 4 L = 1 gallon then you need 2 gallons of paint. I you use the more accurate 3.78 L then
1 gallon = 3.78 L
x gallon = 8 L

3.78 x = 8*1
x = 8/3.78
x = 2.12 gallons.
 
I guess you could say that 1 gallon and 1 L would do you.
8 0
3 years ago
Suppose the value of a car depreciates 8% every year. To the nearest dollar, what will a car that cost $23,995 be worth after 5
Vanyuwa [196]

Answer:

<em>The car will worth $15815 after 5 years.</em>

Step-by-step explanation:

The formula is:    A=P(1+r)^t, where P = Initial cost, A = Final cost,  r = Rate of change in cost per year and  t = Number of years.

Here, P= 23995, t= 5

and r= 8\%=0.08

As here the <u>value of the car depreciates every year, so we need to plug the value of r as negative</u>. So, r=-0.08

Now plugging the above values into the formula, we will get.....

A=23995(1-0.08)^5\\ \\ A=23995(0.92)^5\\ \\ A=15814.6611... \approx 15815

<em>(Rounded to the nearest dollar)</em>

So, the car will worth $15815 after 5 years.

8 0
3 years ago
A shose box measures 15in.by 7in.by 4 an half
Svet_ta [14]
The volume is 472.5in^3.

4 0
3 years ago
Find the break-even point for the given cost and revenue equations. Round to the nearest whole unit. C = 20n + 134,000 R = 160n
Harman [31]
At break-even C = R so we have:-

20n + 134,000 = 160n

140n = 134,000

answer = 134,000 / 140  =  957
8 0
3 years ago
Why should people conserve energy? (Please don’t get the answer form the internet)
Taya2010 [7]
People should conserve energy because it produces a higher quality of life. Reduced emissions result in cleaner air quality. It also helps create a healthier planet and helps sustain resources we have.
7 0
2 years ago
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