Consider the function g(x) = StartLayout Enlarged left-brace first row negative 9, x less-than 11 second row 7, x greater-than-or-equal-to 11 EndLayout.
What is Limit of g (x) as x approaches 11, if it exists?
–9
–1
7
DNE
Answers
The limit as g(x) approaches 11 doesn't exist.
[tex]\lim_{x \to 11} g(x) = DNE[/tex]
It looks like you are working with the following piecewise defined function:
[tex]g(x)=\left \{ {{-9;x<11} \atop {7;x\geq11}} \right.[/tex]
There is a rule in calculus that tells us that for a limit to exist, both lateral limits must be the same as x approaches a given value. This is:
[tex]\lim_{x \to a^{-}} f(x)=\lim_{x \to a^{+}} f(x)[/tex]
if and only if this is true, then:
[tex]\lim_{x \to a^{-}} f(x)=\lim_{x \to a^{+}} f(x)=\lim_{x \to a} f(x)[/tex]
if that condition isn't met, then the limit doesn't exist.
So let's calculate the lateral limits for this function:
[tex]\lim_{x \to 11^{-}} g(x) = -9[/tex]
This means that as x approaches 11 from the left, the function will return a value close to -9
Now, let's calculate the lateral limits for this function:
[tex]\lim_{x \to 11^{+}} g(x) = 7[/tex]
This means that as x approaches 11 from the right, the function will return a value close to 7
You can better visualize this in the graph of the function which I attached to this answer.
Notice that both lateral limits are different, from the left you got a -9 and from the right you got a 7. Therefore, according to the rule I wrote above, the limit does not exist.
For more information on this topic, you can go to the following link:
https://brainly.com/question/17334531?referrer=searchResults
Answer:
D) DNE
Step-by-step explanation:
edge 2021
Related Questions
Which of the pairs of angles are vertical angles and
thus congruent?
ZA and ZG
ZA and B
ZC and E.
ZD and ZH
help please !!
Answers
9514 1404 393
Answer:
∠A and ∠G
∠C and ∠E
Step-by-step explanation:
Vertical angles have the same vertex and are formed from opposite rays. In this figure, the pairs of vertical angles are ...
{A, G}, {B, H}, {C, E}, {D, F}
Of these pairs, the ones listed in your answer choices are ...
∠A and ∠G
∠C and ∠E
An environment engineer measures the amount ( by weight) of particulate pollution in air samples ( of a certain volume ) collected over the smokestack of a coal-operated power plant. Let X1 denote the amount of pollutant per sample when a certain cleaning device on the stack is not operating, and let X2 denote the amount of pollutant per sample when the cleaning device is operating under similar environmental conditions. It is observed that X1 is always greater than 2X2, and the relative frequency behavior of (X1, X2) can be modeled by
f(x,y)= k for 0 <= x <= 2, 0<=y <=1 , 2y<= x and 0 elsewhere
(X and Y are randomly distriibutied over the region inside the tricanle bounded by x=2, y=0 and 2y=x)
a. Find the value of k that makes this a probability desnsity function.
b. Find P >= 3y
Answers
Answer:
[tex]k = 1[/tex]
[tex]P(x > 3y) = \frac{2}{3}[/tex]
Step-by-step explanation:
Given
[tex]f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.[/tex]
Solving (a):
Find k
To solve for k, we use the definition of joint probability function:
[tex]\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1[/tex]
Where
[tex]{ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }[/tex]
Substitute values for the interval of x and y respectively
So, we have:
[tex]\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1[/tex]
Isolate k
[tex]k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1[/tex]
Integrate y, leave x:
[tex]k \int\limits^2_{0} y {dx} \, [0,x/2]= 1[/tex]
Substitute 0 and x/2 for y
[tex]k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1[/tex]
[tex]k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1[/tex]
Integrate x
[tex]k * \frac{x^2}{2*2} [0,2]= 1[/tex]
[tex]k * \frac{x^2}{4} [0,2]= 1[/tex]
Substitute 0 and 2 for x
[tex]k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1[/tex]
[tex]k *[ \frac{4}{4} - \frac{0}{4} ]= 1[/tex]
[tex]k *[ 1-0 ]= 1[/tex]
[tex]k *[ 1]= 1[/tex]
[tex]k = 1[/tex]
Solving (b): [tex]P(x > 3y)[/tex]
We have:
[tex]f(x,y) = k[/tex]
Where [tex]k = 1[/tex]
[tex]f(x,y) = 1[/tex]
To find [tex]P(x > 3y)[/tex], we use:
[tex]\int\limits^a_b \int\limits^a_b {f(x,y)}[/tex]
So, we have:
[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy[/tex]
[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy[/tex]
[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy[/tex]
Integrate x leave y
[tex]P(x > 3y) = \int\limits^2_0 x [0,y/3]dy[/tex]
Substitute 0 and y/3 for x
[tex]P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy[/tex]
[tex]P(x > 3y) = \int\limits^2_0 y/3\ dy[/tex]
Integrate
[tex]P(x > 3y) = \frac{y^2}{2*3} [0,2][/tex]
[tex]P(x > 3y) = \frac{y^2}{6} [0,2]\\[/tex]
Substitute 0 and 2 for y
[tex]P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}[/tex]
[tex]P(x > 3y) = \frac{4}{6} -\frac{0}{6}[/tex]
[tex]P(x > 3y) = \frac{4}{6}[/tex]
[tex]P(x > 3y) = \frac{2}{3}[/tex]
For questions 3 that’s all i need help please !!! For a test and please put your answers below !!! It’s not D because one of friends had took it already and told me he choose D and it was incorrect. Thank you.
Answers
Answer:
56,067
Step-by-step explanation:
there are 52 weeks in a year. and they work 40 hours a week.
[tex]26.96*40=1078\\1078*52=56,067[/tex]
Answer:
The answer is C.
Step-by-step explanation:
What type of angle is angle G?
A. right
B. acute
C. straight
D. obtuse
Answers
Answer:
acute
Step-by-step explanation:
A rectangle has an area of 4(x + 3) square units. x + 3= width, 4=length Use the distributive property to write an equivalent expression for the rectangle's area. Answer _______
Answers
Answer:
4x + 12
Step-by-step explanation:
4*x + 4*3 = 4x + 12
Notice what has happened. The plus sign remains.The 4 multiplies by both the x and the 3That's as far as you can take the problem. You cannot reduce it any further or combine it in any way. The reason is that the x has a 4 in front of it and the 12 has no x.
When those terms are separated by a plus or minus sign, the terms are not the same. Unlike terms cannot be combined.
Answer: 4x+12=4x+12 or 4x+12=4(x+3)
Step-by-step explanation:
(x+3)(4)=4(x+3) *because length x width=areaDistribute 4 into the parenthesis 4x+12=4(x+3)you can go even further4x+12=4x+12Hope this helps!
Pls help me im desperate bots are not supposed to post here
Answers
Answer:
y = [tex]\frac{1}{2}x+8[/tex]
Step-by-step explanation:
From the table given in the picture,
Two points lying on the graph are (-4, 6) and (-2, 7)
Let the linear function is,
y = mx + b
Here, m = slope of the line
b = y-intercept
Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Slope (m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (-4, 6) and (-2, 7) will be,
m = [tex]\frac{7-6}{-2+4}[/tex]
m = [tex]\frac{1}{2}[/tex]
y-intercept is a point for which x = 0
From the given table,
For x = 0, y = 8
Therefore, y-intercept (b) = 8
Equation of the linear function will be,
y = [tex]\frac{1}{2}x+8[/tex]
Determine the amplitude or period as requested. Period of y = - 1/3 * sin 2x
Answers
Answer:
[tex]Period = \pi[/tex]
Step-by-step explanation:
Given
[tex]y = -\frac{1}{3} * \sin(2x)[/tex]
Required
The period
A sine function is represented as:
[tex]y =A \sin(Bx + C) + D[/tex]
Where
[tex]Period = \frac{2\pi}{B}[/tex]
By comparing:
[tex]y =A \sin(Bx + C) + D[/tex] and [tex]y = -\frac{1}{3} * \sin(2x)[/tex]
[tex]B = 2[/tex]
So, we have:
[tex]Period = \frac{2\pi}{2}[/tex]
[tex]Period = \pi[/tex]
Hence, the period of the function is [tex]\pi[/tex]
select all the values of x so g(x) is not a function.
Answers
Step-by-step explanation: We are trying to figure out what makes the chart not a function. A function is is one input equals one output.
so all you have to do is look at the x and look at the number that is already there and just make it repeat.
A bag contains 11 red beads, 10 blue beads, and 4 green beads. If a single bead is picked at random, what is the probability that the bead is green?
Answers
Answer:
4/15
Step-by-step explanation:
PLS HELP
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Answers
Answer:
V= 160 ft
Step-by-step explanation:
First 10×8×6 then ÷ 3 = 160
In circle M, decanted PAMD and PBC are drawn from point P such that
Angle BC = 100 Degrees
Angle CD = 62 Degrees
Which of the following is the measure of angle P?
1. 19
2. 22
3. 34
4. 40
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Answer:
Step-by-step explanation:
Need help fast please, plz
Answers
Answer:
13. rational, integer, white number, natural
14. irrational
Step-by-step explanation:
the third root of 125 is 5.
so, it is everything of the list except for irrational.
pi is a prime example of an irrational number. any calculation not eliminating the irrational number is also irrational.
find two mixed number or fractions that have a quotient of 3 1/5
Answers
Answer:
[tex]6 \frac{1}{5} [/tex]
Step-by-step explanation:
31/5
6/1/5
15w, when w = 12 I need help plz
Answers
Answer:
180...
Step-by-step explanation:
15 x 12 = 180
50 pts please help asap !
Answers
Answer:
its 23.5
Step-by-step explanation:
Answer:
d 26
Step-by-step explanation:
AC=24
AB=AC/2=12
AD²=AB²+BD²
AD²=5²+12²=25+144=169
AD=√169=13
AE=2*13=26
The coordinates of the following points represent the vertices of a rectangle. E: (4,2) F: (10,2) G: (10,8) H: (4,8) What is the perimeter, in units, of rectangle EFGH?
Answers
Answer:
Perimeter of rectangle EFGH = 24 unit
Step-by-step explanation:
Given:
E: (4,2)
F: (10,2)
G: (10,8)
H: (4,8)
Find:
Perimeter of rectangle EFGH
Computation:
Distance = √(x1 - x2)² + (y1 - y2)²
Distance between EF = √(4 - 10)² + (2 - 2)²
Distance between EF = √36
Distance between EF = 6units
Distance between FG = √(10 - 10)² + (2 - 8)²
Distance between FG = √36
Distance between FG = 6 units
Distance between GH = √(10 - 4)² + (8 - 8)²
Distance between GH = √36
Distance between GH = 6 units
Distance between HE = √(4 - 4)² + (8 - 2)²
Distance between HE = √36
Distance between HE = 6 units
Perimeter of rectangle EFGH = 6 + 6 + 6 + 6
Perimeter of rectangle EFGH = 24 unit
This composite figure is made up of three simpler shapes. What is the area of
the figure?
7 cm
4 cm
5 cm
4 CE
8 cm
A. 66 square cm
R 50 square cm
C. 46 square cm
D. 80 square cm
Answers
Answer:
A. 66 square cm
Step-by-step explanation:
HOPE IT HELPSS! :D
please help only with number one
Answers
Answer:
so, where the dotted line is that is called the height, so you would times it and find your answer.
Tell whether the angles are complementary or supplementary. Then find the value of x.
Answers
Answer:
[tex]1) 3x+45=90[/tex]
[tex]3x=90-45[/tex]
[tex]3x=45[/tex]
[tex]\frac{3x}{3} =\frac{45}{3}[/tex]
[tex]x=15[/tex]
1) The angles are complementary
[tex]--------[/tex]
[tex]2)x-20+x=90\\[/tex]
[tex]2x=90+20[/tex]
[tex]2x=110[/tex]
[tex]x=55[/tex]
2) The angles are complementary
[tex]--------[/tex]
[tex]3)2x+(3x+25)=180[/tex]
[tex]2x+3x+25=180[/tex]
[tex]2x+3x=180-25[/tex]
[tex]5x=155[/tex]
[tex]x=\frac{155}{5}[/tex]
[tex]x=31[/tex]
3) The angles are supplementary
[tex]----------[/tex]
hope it helps..
have a great day!!
y = x + 1 how many solutions does this system have
Answers
Answer:
Step-by-step explanation:
There are an infinite number of solutions.
write the first five terms of the sequence an=3n^2
Answers
Answer:
2,1,0 is the sequence of its terms
Complete the missing parts of the table for the following function y=7^x
Answers
Answer:
x= -2 y = ([tex]\frac{1}{49}[/tex])
x= 0 y = 1
x= 2 y = 49
Step-by-step explanation:
x= -2 -> (7)² = 49, negative power makes it inverse to a fraction
y = ([tex]\frac{1}{49}[/tex])
x= 0 -> anything to the power of 0 is always 1
y = 1
x= 2 -> 7² = 7 × 7 = 49
y = 49
Sarah has 35 paperback books and 20 hardback books.
What fraction of the books are hardback
Answers
Answer:
4/11...................
Answer: 4/11
Step-by-step explanation:
The total number of books is 35+20=55, which will be the denominator, because the question is asking what fraction of all the books are hardcover. The number of hardcover books, 20, will be the numerator, so we end up with the fraction 20/55. 20 and 55 are both divisible by 5 (this means that when divided by 5, both numbers have a whole number quotient). 20/5= 4 and 55/5=11
So, the answer is 4/11
Find the LCD of the following:
1. 3/8, 1/4, 5/12
2. 2/3,5/6, 7/9
Answers
Answer:
1. LCD= 24
2. LCD= 18
fr plz help i give brainiest
Answers
Answer:
Hello Love! Answer: 8000
volume is just length x width x height
so 20 x 20 x 20 = 8000
Answer:
8,000 in³
Step-by-step explanation:
All you have to do is multiply all the sides so it would be
20 · 20 · 20 = 8,000 in³
Hope this helped.
If you are willing to give me a brainliest you can its your choice.
I just need one more to level up.
Well anyways
STAY SAFE!!!!!
What’s the answer to this question?
Answers
what is the surface area of this design
Answers
Answer:
the correct answer is 197 in^2
5.08x1.2/1.90+2.0-3.0001=?
Answers
Answer:
2.20832105263
i think it is
Answer:
6.774086
Step-by-step explanation:
The following graph shows the fuel efficiency of a sample of cars. How many
cars get between 10 and 15 miles per gallon?
Fuel Efficiency of Cars
40
35
30
25
20
Number of cars
15
10
0
5
10
15
25
30
20
Miles per gallon
O A. 15
O B. 20
C. 5
D. 40
Answers
Answer:
B) 20
The 10-15 x axis bar graph shows 20 cars on the y axis
can anyone help explain how to solve this?? please
Answers
Answer:
C
Step-by-step explanation:
All four sides of the triangle are 4 cm. An equilateral triangle has equal sides