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
11Alexandr11 [23.1K]
3 years ago
5

Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2. ​

Mathematics
1 answer:
insens350 [35]3 years ago
6 0

Answer:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

Step-by-step explanation:

Given

p(x) = \frac{x^2-2x-3}{x+2} -- Missing from the question

Required

The behavior of the function around its vertical asymptote at x = -2

p(x) = \frac{x^2-2x-3}{x+2}

Expand the numerator

p(x) = \frac{x^2 + x -3x - 3}{x+2}

Factorize

p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}

Factor out x + 1

p(x) = \frac{(x -3)(x + 1)}{x+2}

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

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

As x approaches -2 implies that:

x -> -2^{-} Say x = -3

p(x) = \frac{(x -3)(x + 1)}{x+2}

p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

x->-2^{-}, p(x)->-\infty

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: x>-2

Say x = -2.1

p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

x->-2^{+}, p(x)->-\infty

So, the behavior is:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

You might be interested in
Which equation best represents the line in the graph​
bulgar [2K]
Answer:

G

Explanation
4 0
3 years ago
Find the missing coefficient.
lawyer [7]
<span>(2d - 5)(2d - 4) = 4d^2 - 2d x 4 - 5 x 2d + 20 = 4d^2 - 18d + 20

Answer is B
Hope it helps! </span>
3 0
3 years ago
Read 2 more answers
The ratio of white socks to brown socks is <br> PLZ HELP ASAP
Alex73 [517]

Answer:

0.875 is the ratio from white to brown socks.

6 0
3 years ago
A recipe uses 800 grams of nuts with 160 grams of butter. If you only have 500 grams of nuts. How many grams of butter should yo
Alinara [238K]

Answer:

100

Step-by-step explanation:

800÷500

160÷1.6

.....

8 0
3 years ago
Read 2 more answers
Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by y=√x and y=x^2. Find V either by sl
Ede4ka [16]

Answer:

The volume of the solid is 3\pi/10

Step-by-step explanation:

In this case, the washer method seems to be easier and thus, it is the one I will use.

Since the rotation is around the y-axis we need to change de dependency of our variables to have f(x)\rightarrow f(y). Thus, our functions with y as independent variable are:

x=\sqrt{y}\\ x=y^2

For the washer method, we need to find the area function, which is given by:

A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]

By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function x=\sqrt{y} and the inner one by x=y^2. Thus, the area function is:

A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)

Now we just need to integrate. The integration limits are easy to find by just solving the equation \sqrt(y)=y^2, which has two solutions y=0 and y=1. These are then, our integration limits.

V=\pi\int_{0}^1 (y-y^4)dy\\ V=\pi (\int_{0}^1 ydy - \int_{0}^1 y^4dy)\\ V=\pi/2-\pi/5\\\boxed{V=3\pi/10}

3 0
3 years ago
Other questions:
  • 4h2 - 2h + 6 for h = ‐2?
    11·1 answer
  • 983.53 in a fraction and word form
    15·1 answer
  • What are the solutions to 2(x-7)^2 = 32?
    9·1 answer
  • Look at the picture and answer the question
    6·1 answer
  • Is this a function? I will mark you as most brilliance if you get this right!
    14·1 answer
  • Follow this link to view Juan’s work. Critique Juan’s work by justifying correct solutions and by explaining any errors he made.
    14·1 answer
  • 4. A movie-streaming service offers 12 children's movies. This is 15% of the
    10·1 answer
  • 4
    8·1 answer
  • 5.
    13·1 answer
  • Which of the following functions has an initial value of -1/2 and a rate of change of 0?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!