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MA_775_DIABLO [31]
3 years ago
11

G prove that limx→∞(x 2 + 1)/x2 = 1 using the definition of limit at ∞.

Mathematics
1 answer:
Maslowich3 years ago
7 0
\displaystyle\lim_{x\to\infty}\frac{x^2+1}{x^2}=1

means to say there is some number M for which any choice of \varepsilon>0 such that

x>M\implies\left|\dfrac{x^2+1}{x^2}-1\right|

Working backwards, we have

\left|\dfrac{x^2+1}{x^2}-1\right|=\left|1+\dfrac1{x^2}-1\right|=\dfrac1{x^2}
\implies\sqrt{\dfrac1{x^2}}

So, whenever x>M=\dfrac1{\sqrt\varepsilon}, we can always guarantee that \left|\dfrac{x^2+1}{x^2}-1\right|.
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For the x-values 1, 2, 3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of
Elan Coil [88]

Answer:

Option A: Exponential growth

Step-by-step explanation:

If  for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.

Option B is incorrect because  because y is not decreasing

Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.

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4 years ago
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The segments shown below could form a triangle.<br><br> A. True<br> B. False
suter [353]

answer TRUE because they would make a triangle

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3 years ago
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Hisako sells dolls at her doll store. If she sells a doll for $35, and there is 6% sales tax, what is the tax amount a customer
Sloan [31]

Given:

The price of a doll = $35

Sales tax = 6%

To find:

The tax amount that a customer will pay on one doll.

Solution:

The price of doll is $35 and the sales tax is 6%, so the tax amount on a doll is 6% of 35.

\text{Tax amount}=35\times \dfrac{6}{100}

\text{Tax amount}=\dfrac{210}{100}

\text{Tax amount}=\dfrac{21}{10}

\text{Tax amount}=2.1

Therefore, the tax amount that a customer will pay on one doll is $2.1.

7 0
3 years ago
In ΔEFG, the measure of ∠G=90°, EF = 95 feet, and FG = 26 feet. Find the measure of ∠F to the nearest degree.
Firdavs [7]

Answer:

74.4°

Step-by-step explanation:

Given

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  • EF = 95 feet
  • FG = 26 feet

Use sine law to find ∠F

As we know:

Sin(GEF)/ GF = Sin(EGF)/EF

<=> Sin(GEF) / 26 = Sin(90)/95

<=>Sin(GEF) / 26 = 1/95

<=> Sin(GEF)  = 26/95

<=> ∠GEF ≈ 15.8°

=> ∠F = 180° - ∠G - ∠GEF

∠F = 180° - 90° - 15.8° = 74.4°

3 0
3 years ago
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In 20 words or fewer, can 8 • 7 • 6 be written as 8! . . . and why or why not?
grin007 [14]

Answer:

No, because factorials are product of all positive integers less than or equal to a given positive integer.

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