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
AVprozaik [17]
3 years ago
6

Identify the functions that are continuous on the set of real numbers and arrange them in ascending order of their limits as x t

ends to 5. Please look at the attached image.

Mathematics
1 answer:
Studentka2010 [4]3 years ago
6 0

Answer:

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

Step-by-step explanation:

1.f(x)=\frac{x^2+x-20}{x^2+4}

The denominator of f is defined for all real values of x

Therefore, the function is continuous on the set of real numbers

\lim_{x\rightarrow 5}\frac{x^2+x-20}{x^2+4}=\frac{25+5-20}{25+4}=\frac{10}{29}=0.345

3.h(x)=\frac{3x-5}{x^2-5x+7}

x^2-5x+7=0

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function h is defined for all real values.

\lim_{x\rightarrow 5}\frac{3x-5}{x^2-5x+7}=\frac{15-5}{25-25+7}=\frac{10}{7}=1.43

2.g(x)=\frac{x-17}{x^2+75}

The denominator of g is defined for all real values of x.

Therefore, the function g is continuous on the set of real numbers

\lim_{x\rightarrow 5}\frac{x-17}{x^2+75}=\frac{5-17}{25+75}=\frac{-12}{100}=-0.12

4.i(x)=\frac{x^2-9}{x-9}

x-9=0

x=9

The function i is not defined for x=9

Therefore, the function i is  not continuous on the set of real numbers.

5.j(x)=\frac{4x^2-7x-65}{x^2+10}

The denominator of j is defined for all real values of x.

Therefore, the function j is continuous on the set of real numbers.

\lim_{x\rightarrow 5}\frac{4x^2-7x-65}{x^2+10}=\frac{100-35-65}{25+10}=0

6.k(x)=\frac{x+1}{x^2+x+29}

x^2+x+29=0

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function k is defined for all real values.

\lim_{x\rightarrow 5}\frac{x+1}{x^2+x+29}=\frac{5+1}{25+5+29}=\frac{6}{59}=0.102

7.l(x)=\frac{5x-1}{x^2-9x+8}

x^2-9x+8=0

x^2-8x-x+8=0

x(x-8)-1(x-8)=0

(x-8)(x-1)=0

x=8,1

The function is not defined for x=8 and x=1

Hence, function l is not  defined for all real values.

8.m(x)=\frac{x^2+5x-24}{x^2+11}

The denominator of m is defined for all real values of x.

Therefore, the function m is continuous on the set of real numbers.

\lim_{x\rightarrow 5}\frac{x^2+5x-24}{x^2+11}=\frac{25+25-24}{25+11}=\frac{26}{36}=\frac{13}{18}=0.722

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

You might be interested in
Find the tenth term in the following geometric sequence. 8, 4, 2, 1, . . .
Marrrta [24]

Answer:

  c)  0.0156

Step-by-step explanation:

The general term a[n] of a geometric sequence is given in terms of the first term a[1] and common ratio r as ...

  a[n] = a[1]r^(n-1)

The given sequence has an initial term of a[1]=8 and a common ratio of 4/8=1/2. Then the general term is ...

  a[n] = 8(1/2)^(n-1)

The 10th term is then ...

  a[10] = 8(1/2)^(10-1) = 8(1/2)^9 = 8/512

  a[10] = 0.015625 ≈ 0.0156

7 0
3 years ago
Someome help me plsssssssssssssssssss
vodomira [7]
Volume formula is WxHxL so 3/2 times 4 times 1/2 is 3, the answer is 3 cm^3
3 0
2 years ago
There are 42 kids on the playground. Then 26 more kids come out to join them. How many kids are now on the playground all togeth
aev [14]

Answer:

68

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Luke added 429 + 699 +314 and got 950.Is this sum reasonable?
trasher [3.6K]
No, it's not reasonable
6 0
3 years ago
Read 2 more answers
Of Bernie's insect collection, 15 out of 25 insects are butterflies. Which of the following is not another way of expressing 15
koban [17]
B is the answer for ur question :D
8 0
3 years ago
Other questions:
  • A rectangular park has an area of 64 square yards. If we multiply its length and width by 12, what will be the area of the new r
    14·2 answers
  •  Find the sum ​(33x+99​)+​(minus−44x+88​)
    10·1 answer
  • How to simplify the expression 7x+15x
    12·2 answers
  • What is the value of x in the following system of equations? 11x + 12y = 13 14x + 15y = 16 A. x = −2 B. x = −1 C. x = 1 D. x = 2
    14·1 answer
  • If a carpet sells for $15.50 per square yard, how much will it cost to cover a room
    9·2 answers
  • Gordon purchased a television when his local electronics store had a sale. The television was offered at 30% off its original pr
    14·1 answer
  • Use the values in the table to determine the slope.
    14·2 answers
  • Brianna is crocheting a scarf as a birthday present for her sister. She started the scarf yesterday and needs to finish it today
    6·1 answer
  • Determine if they following is systems of equations?<br> y = 3x + 2<br> y = 7x -10
    8·1 answer
  • 8select all correct answers what is 9,150, 000, 000, 000, 000, 000 Express in scientific notation
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!