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
iren2701 [21]
1 year ago
11

Calculus piecewise function. ​

Mathematics
1 answer:
Kipish [7]1 year ago
4 0

Part A

The notation \lim_{x \to 2^{+}}f(x) means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows \lim_{x \to 2^{+}}f(x) = 2

Then for the left hand limit \lim_{x \to 2^{-}}f(x), we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, \lim_{x \to 2^{-}}f(x) = 1

===============================================================

Part B

Because \lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x) this means that the limit \lim_{x \to 2}f(x) does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since \lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3, this means the limit \lim_{x \to 4}f(x) does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

You might be interested in
Lainey bought a set of 20 makers for $6 what is the cost of 1 marker? <br>​
loris [4]

Answer:

0.30

Step-by-step explanation:

$6 Total

20 markers

6/20=0.30

0.3 per maker.

Cost of 1 marker is $0.30

6 0
3 years ago
A square piece of cheese covers 10 square inches of a plate. What is the approximate length of one side of the piece of cheese?
Airida [17]

Answer:

3.16 inches

Step-by-step explanation:

Sqrt 10 = 3.16 inches

3 0
2 years ago
Read 2 more answers
A stock has had returns of 7 percent, 25 percent, 17 percent, −13 percent, 25 percent, and −6 percent over the last six years. W
Tems11 [23]

Answer: Geometric average return would be 0.10% and arithmetic average return would be 9.17%.

Step-by-step explanation:

Since we have given that

Returns are as follows:

7%, 25%, 175, -13%, 25% and -6%.

Geometric return is given by

\sqrt[6]{(1+0.07)(1+0.25)(1+0.17)(1-0.13)(1+0.25)(1-0.06)}-1\\\\=\sqrt[6]{(1.17)(1.25)(1.17)(0.87)(1.25)(0.94)}-1\\\\=0.097\%=0.10\%

Arithmetic average return would be

\dfrac{7+25+17-13+25-6}{6}=9.17\%

Hence, geometric average return would be 0.10% and arithmetic average return would be 9.17%.

7 0
3 years ago
Plz solve this question for me
sveticcg [70]

Answer:

2

Step-by-step explanation:

w + 1/2 ➡ (2w + 1)/2

w/4 + 2➡ (w + 8)/4

(2w + 1)/2 = (w + 8)/4

8w + 4 = 2w + 16 ➡ 6w = 12

w = 2

3 0
3 years ago
Read 2 more answers
1. What values of a, b, and c would you use in the quadratic formula for the following equation?
Archy [21]
Question (1):
The general formula of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
5x² + 9x = 4
Rearrange the given equation to look the standard one:
5x² + 9x - 4 = 0
Now, compare the coefficients in the given equation with the standard one, you will find that:
a = 5, b = 9 and c = -4

Question (2):
The given expression is:
 -5 + 2x²<span> = -6x 
</span>Rearrange this expression to be in standard form:
2x² + 6x - 5 = 0
This means that:
a = 2
b = 6
c = -5
The roots of the equation can be found using the formula in the attached image.
Substituting in this formula with the given a, b and c, we would find that the correct choice is third one (I have attached the correct choice)

Question (3):
Quadratic formula (the one used in the previous question, also shown in attached images) is the best method to get the solution of any quadratic equation. This is because, putting the equation in standard form, we can simply get the values of a, b and c, substitute in the formula and get the precise solutions of the equation.

Hope this helps :)

8 0
3 years ago
Read 2 more answers
Other questions:
  • Chase is 57 years younger the. Kori. 8 years ago Kori age was 4 times Chase age. how old is chase
    11·2 answers
  • phillip watched a beach volleyball game from 1:45 pm to 2:00pm how many degrees did the minute hand turn?
    6·1 answer
  • What is 9/10 divided by 3/12
    9·1 answer
  • A ball is thrown in the air from a ledge. Its height in feet is represented by
    6·1 answer
  • Long division 40.8 divided by 4
    5·1 answer
  • F(t) = 2t - 3 evaluate the function
    14·1 answer
  • Divide £945 in the ratio 2:5
    13·1 answer
  • The triangle pictured below represents a community garden, which is surrounded on
    13·2 answers
  • Lauren can spend no more then 10$ at a video game arcade. Each game in the arcade costs 0.25$
    13·1 answer
  • Can someone help me out? Will mark brainiest
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!