1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Maru [420]
3 years ago
13

Let f (x) = 3x − 1 and ε > 0. Find a δ > 0 such that 0 < ∣x − 5∣ < δ implies ∣f (x) − 14∣ < ε. (Find the largest

such δ.) What limit does this prove?
Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
3 0

Answer:

This proves that f is continous at x=5.

Step-by-step explanation:

Taking f(x) = 3x-1 and \varepsilon>0, we want to find a \delta such that |f(x)-14|

At first, we will assume that this delta exists and we will try to figure out its value.

Suppose that |x-5|. Then

|f(x)-14| = |3x-1-14| = |3x-15|=|3(x-5)| = 3|x-5|< 3\delta.

Then, if |x-5|, then |f(x)-14|. So, in this case, if 3\delta \leq \varepsilon we get that |f(x)-14|. The maximum value of delta is \frac{\varepsilon}{3}.

By definition, this procedure proves that \lim_{x\to 5}f(x) = 14. Note that f(5)=14, so this proves that f is continous at x=5.

You might be interested in
The following table shows scores obtained in an examination by B.Ed JHS Specialism students. Use the information to answer the q
Makovka662 [10]

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

\frac{\sum f}{4}=\frac{100}{4}=25

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF)_{p} = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h

     =34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75

The value of first quartile is 34.75.

Q₃ is at the position:

\frac{3\sum f}{4}=\frac{3\times100}{4}=75

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF)_{p} = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h

     =44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83

The value of third quartile is 44.83.

Then the inter-quartile range is:

IQR = Q_{3}-Q_{1}

        =44.83-34.75\\=10.08

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}

                                 =\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89

Thus, the probability that a student scored at most 50 on the examination is 0.89.

5 0
3 years ago
A chain of sports shops catering to beginning skiers, headquartered in Aspen, Colorado, plans to conduct a study of how much a b
Hitman42 [59]

Answer:

47.4 ;

50

Step-by-step explanation:

Given the data :

X ($) : 85 139 161 175 85 133 149 145 136 131 290 235 132 149 322 214 105 90 162 229 121 113 149 126139 118 156 214 172 87 172 230 195 126 128 142 118 139

The smallest class interval :

Range / number of classes

Number of classes to use = 5

Range = Maximum - Minimum = (322 - 85) =237

Hence, smallest class interval :

237 / 5 = 47.4

A better class interval would be, one without decimal, rounded to the nearest 10; this will be easier and make more statistical sense

Hence, smallest class interval rounded to the nearest 10 :

47.4 = 50 (nearest 10)

3 0
2 years ago
Lena estimated the height of a desk to be 38 inches. The actual height is 41 inches.
Leno4ka [110]

Answer:

7.3%

Step-by-step explanation:

First you have to find out what 38 out of 41 is as a percentage

This is 92.68%

so now we have to do

100.00 - 92.68 this is 7.32

But you said round to the nearest tenth so it would actually be rounded down to 7.3%

4 0
2 years ago
Read 2 more answers
May you please help me for part b for brainliest,
olya-2409 [2.1K]

Answer:

Very certain it is C

Step-by-step explanation:

There are no points on the graph line itself so I cannot really confirm this but i am 70% sure

7 0
3 years ago
There are five people sitting around the dinner table .each person has 2/10of a pie on their plate .how much pie is left ?explai
agasfer [191]
No pie is left because 2/10 multiplied by 5 is 10/10, or 1 whole pie, so none of the pie is left.


please mark as brainliest or give good rating if this helped you. I hope it did!
4 0
3 years ago
Read 2 more answers
Other questions:
  • A. Scalene<br> B. Obtuse<br> C. Equilateral <br> D. Isosceles <br> E. Acute<br> F. Right
    6·1 answer
  • A state lottery randomly chooses 8 balls numbered from 1 through 37 without replacement. You choose 8 numbers and purchase a lot
    5·1 answer
  • Find the values of k so that the slope of he line joining (5,k) and (6,k^2) is 30.
    15·1 answer
  • Don't comment unless u can help!
    7·1 answer
  • Find the slope and y-intercept of the line.<br><br> 12x + 2y = –60
    13·1 answer
  • Find the surface area of a square pyramid with base length of 16 cm and a slant height of 20 cm
    11·1 answer
  • Solve for x.<br><br> + 1 = 3<br><br> x = 1 <br> x = 2 <br> x = 3<br> x = 6
    7·2 answers
  • Evaluate all numerical expressions with exponents
    12·1 answer
  • Jade is buying a dress for winter formal. Tax was $4.30 and her total bill was $63 with tax included. How much was the dress?
    14·1 answer
  • Which expression gives the surface area of a sphere with radius r?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!