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
Maksim231197 [3]
2 years ago
12

Can someone help me with this? I need to find the points of discontinuity/limits for each of these. I think one point is 4, but

I'm not sure about the others.

Mathematics
1 answer:
Debora [2.8K]2 years ago
6 0
The answers are shown in the attached image

-------------------------------------------------------------------------

Explanation:

Set the denominator x^4-8x^3+16x^2 equal to zero and solve for x

x^4-8x^3+16x^2 = 0
x^2(x^2-8x+16) = 0
x^2(x-4)^2 = 0
x^2 = 0 or (x-4)^2 = 0
x = 0 or x-4 = 0
x = 0 or x = 4

The x values 0 and 4 make the denominator zero

These x values lead to asymptote discontinuities because the numerator 8x-24 = 8(x-3) has no common factors which cancel with the denominator factors.

There are two vertical asymptotes

Let's see what happens when we plug in a value to the left of x = 0, say x = -1, we'd get
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(-1) = (8(-1)-24)/((-1)^4-8(-1)^3+16(-1)^2)
f(-1) = -1.28
So as x gets closer and closer to x = 0 from the left side, the f(x) is heading to negative infinity

Now plug in some value to the right of x = 0. I'm going to pick x = 1
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(1) = (8(1)-24)/((1)^4-8(1)^3+16(1)^2)
f(1) = -1.78 (approximate)
So as x gets closer and closer to x = 0 from the right side, the f(x) is heading to negative infinity

Overall, as x approaches 0 from either the left or right side of x = 0, the y value is heading off to negative infinity

---------------------

Repeat for values to the left and right of x = 4
We can't use x = 1 as it turns out that x = 3 is a root
But we can use something like x = 3.5 to find that...
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(3.5) = (8(3.5)-24)/((3.5)^4-8(3.5)^3+16(3.5)^2)
f(3.5) = 1.31 approx
So as x gets closer to x = 4 from the left, y is getting closer to positive infinity

Plug in x = 5 to find that
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(5) = (8(5)-24)/((5)^4-8(5)^3+16(5)^2)
f(5) = 0.64
which has the same behavior as the left side

So overall, as we approach x = 4, the y value is heading off to positive infinity

Again everything is summarized in the image attachment

Note: you could make a table of more values but they would effectively say what has already been said. It would be redundant busy work. However, its always good practice for function evaluation. 

You might be interested in
How do you find the x
lions [1.4K]
Because those are straight lines, the 46 degrees must be equal to the (2x - 4).
2x -4 = 46.
2x = 46 + 4
2x = 50
x = 50/2
x = 25.
7 0
3 years ago
. <br> What is the value of x?<br> A;90<br> B;225<br> C;180 <br> D;135
Ludmilka [50]
The answer is 180 degrees. 

A right angle formed at the edge of any circle will always create an arc of 180 degrees. This is true no matter where it is placed and no matter the side lengths. 
8 0
3 years ago
I will give brainliest
pshichka [43]

Answer:

They studied for a little more than an our. A

Step-by-step explanation:

Because if you multiply 4 on 2/3 you get 8/12, then add 8/12 and 7/12 together to get 15/12 simplified 1  3/12.

3 0
2 years ago
Read 2 more answers
PLEASE LOOK at the photo and help me on these 2 questions :(!!!!!
Tems11 [23]

Answer:

1) f(g(2)) = 24

2) f(g(-1)) = -4

Step-by-step explanation:

1) GIven f(x) = x²+2x and g(x) = 2x

f(g(x)) = f(2x)

f(2x) = (2x)² + 2(2x)

f(2x) = 4x² + 4x

f(g(x)) = 4x² + 4x

f(g(2)) = 4(2)² + 4(2)

f(g(2)) = 16+8

f(g(2)) = 24

2) f(x) = x+1 and g(x) = 5x

f(g(x)) = f(5x)

f(5x)= 5x + 1

f(g(x)) = 5x + 1

f(g(-1)) = 5(-1) + 1

f(g(-1)) = -5+1

f(g(-1)) = -4

8 0
3 years ago
It costs $68 for 16 square feet of flooring. How much does it cost for 12 square feet of flooring?
belka [17]
We know that it costs $68 for 16 square feet of flooring. To find out how much it costs for 12, we first have to find out how much it costs for 1 square foot.
To find that, we would do $68 divided by 16, which is 4.25.
That means 1 square foot costs $4.25.
Then, we would multiply $4.25 by 12 to find how much 12 square feet costs.
$4.25 times 12 is 51.

So, it would cost $51 to have 12 square feet of flooring.
5 0
3 years ago
Other questions:
  • 15. An airplane dimbs at an angle of 12 with the ground. Find the horizontal distance it has traveled
    9·1 answer
  • If x=8 and y=14. Find y when x=48​
    13·1 answer
  • 26,143,062 expanded form
    9·2 answers
  • 4gallons is how many cups of milk​
    5·2 answers
  • Find the average of the following numbers: * What is the average of the first n positive even numbers?
    12·1 answer
  • PLEASE ANSWER CORRECTLY AND BRAKE DOWN ASAP PLEASE!!The other options is 1 and the other is 1 1/6.
    11·1 answer
  • If x = 2a - b^2, then b equals
    7·1 answer
  • Please help me with this
    12·1 answer
  • A sequence is defined by the recursive function f(n + 1) = f(n). It f(3) = 9, what is f{1) ?
    5·1 answer
  • 517.8 is what percent of 384?Round to the nearest hundredth.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!