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
I WILL AWARD BRAINLIEST!! PLEASE HELP!!!<br> Find the areas of the trapezoids.
Galina-37 [17]

Answer:

A = 12 units ^2

Step-by-step explanation:

The area of the trapezoid is found by

A = 1/2 (b1+b2)h

b1 = 2

b2 = 4

h = 4

I found these by looking at the graph

A = 1/2(2+4) 4

A = 1/2(6*4)

A = 12 units ^2

8 0
3 years ago
154 and 145 to the nearest hundred
Yuki888 [10]

Answer: 154: 200 145: 100

Step-by-step explanation:

If the number next to the place value is 5 or more you round it up. Like I did 154. But if the number is less that 5 you put everything to zero EXCEPT for the place value you are rounding. Good Luck

5 0
2 years ago
Read 2 more answers
3. (04.04 MC)
Marina CMI [18]

Answer:

Part A:

The graph passes through (0,2) (1,3) (2,4).

If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points. Using (0,2) and (1,3). Write in slope-intercept form, y=mx+b. y=x+2

Using (0,2) and (2,4). Write in slope-intercept form, y=mx+b. y=x+2. They are the same and in graph form, it gives us a straight line.

Since the slope is constant (the same) everywhere, the function is linear.

Part B:

A linear function is of the form y=mx+b where m is the slope and b is the y-intercept.

An example is  y=2x-3

A linear function can also be of the form ax+by=c where a, b and c are constants. An example is 2x + 4y= 3

A non-linear function contains at least one of the following,

*Product of x and y

*Trigonometric function

*Exponential functions

*Logarithmic functions

*A degree which is not equal to 1 or 0.

An example is...xy= 1 or y= sqrt. x

An example of a linear function is 1/3x = y - 3

An example of a non-linear function is y= 2/3x

3 0
3 years ago
Please help me with the question below
loris [4]

Answer:

The answer is A.

Step-by-step explanation:

This is because Tia's amount of money minus Dana's amount of money should be at least 5

6 0
3 years ago
Samuel used 1/5 of an ounce of butter to make 1/15 of a pound of jelly. How many ounces of butter are needed to make a pound of
vredina [299]
Set up ratio problem

.2 oz butter / (1/15) lb jelly = x / 1 lb jelly

Then cross multiply the stuff opposite each other in the fractions... set it up as a multiplication problem

.2 × 1  = (1/15) × x 

.2 = (1/15)x

Multiply both sides of equation by 15 to clear out the (1/15) fraction and get x 

x = 3
8 0
3 years ago
Other questions:
  • A^3b^2 divided by a^-1b^-3
    13·1 answer
  • 7x2–5 - 28-3+5.
    5·2 answers
  • Helpppppp mathhhhhhhhh
    9·1 answer
  • I need help in all of the questions 7-16
    11·1 answer
  • I will award brainliest.<br> Complete the table! Thanks
    6·1 answer
  • 13, 5, 4, 9, 7, 14, 4 The deviations are _____.
    7·1 answer
  • 6 x 1/4 Multiply 1/4 how many times? Move from 0 to where. Product:
    14·1 answer
  • A candy jar contains pieces of cherry and cinnamon candy. Seventy five percent of the candies
    8·1 answer
  • The population of a small town was 3500 in 2005. The population increases by 4% annually. A. Write an exponential growth functio
    12·1 answer
  • What is 26% of 200.i really need to know
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!