Given StartLayout Enlarged left-brace First-row StartFraction x cubed minus 1 Over x squared minus 1 EndFraction, for x less-than 1 second row StartFraction 3 Over x minus 1 EndFraction, for x greater-than-or-equal-to 1 EndLayout. What is Limit of f (x) as x approaches 1 minus?
Negative three-halves
0
Three-halves
DNE
Answers
Answer:
Its C 3/2 just did the test
Step-by-step explanation:
The value of the [tex]\lim_{ x \rightarrow 1^-}f(x)[/tex] is ∞, since option (d) DNE.
What is function?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
How to evaluate the [tex]\lim_{ x \rightarrow 1^-}f(x)[/tex]?The given function is [tex]f(x)=\left\{\begin{array}{l}\frac{x^{3}-1}{x^{2}-1}, \text { for } x < 1 \\\frac{3}{x-1}, \text { for } x \geq 1\end{array}\right[/tex].
We need to evaluate the value of [tex]\lim_{ x \rightarrow {1^-}}f(x)[/tex].
So [tex]\lim_{ x \rightarrow {1^-}}f(x)=\lim_{ x \rightarrow {1}}(\frac{3}{x-1})[/tex]
[tex]=\frac{3}{1-1}[/tex]
[tex]=\frac{3}{0}[/tex]
= ∞
Hence the value of the function is ∞.
Learn more about the function on https://brainly.com/question/12431044
#SPJ2
Related Questions
Please help!
A circle is defined by the equation below:
x^2 + y^2 - x - 2y - 11/4 = 0
What are the coordinates for the center of the circle and the length of the radius?
Answers
Answer:
Step-by-step explanation:
We know that the equation of a circle is:
(
x
−
a
)
2
+
(
y
−
b
)
2
=
R
2
where a and b are the coordinates of the center, and R is the radius.
So in this question we have to complete the squares:
x² + y² - x - 2y - 11/4 = 0 ->
x² - x + 1/4 + y² - 2y = 11/4 +1/4 ->
(x - 1/2)² + y² - 2y + 1 = 12/4 + 1 ->
(x - 1/2)² + (y - 1)² = 4
Therefore, the coordinates of the center are C = ( 1/2, 1) and the Radius is R = 2
x² + y² - x - 2y - 2³/₄ = 0
x² + y² - x - 2y = 2³/₄
x² - x + y² - 2y = 2³/₄
(x² - x + 1) + (y² - 2y + 4) = 2³/₄ + 1 + 4
(x - 1)² + (y - 2)² = 7³/₄
The coordinates for center of the circle is equal to (1, 2). The coordinates of the length of the radius is √(³¹/₄).
Math help please show all work thank you !
Answers
9514 1404 393
Answer:
W = 55°X = 125°Y = 110°Z = 70°Step-by-step explanation:
Corresponding angles in similar figures are congruent. Corresponding angles are listed in the same order in the similarity statement.
∠A = ∠W = 55°
∠B = ∠X = 125°
∠C = ∠Y = 110°
∠D = ∠Z = 70°
In a grade seven class, 18 students have pets, and 12 do not. What percent of the class has a pet?
I will mark brainliest to the first correct answer
urgent pls
Answers
If 18+12 is 30 and only 18 of them has pets then 70 percent have pets
$70,000 - 17 1/2 % .
if i get this right i get the iphone xr
Answers
Answer:
$57750
Step-by-step explanation:
$70,000 - 17.5%
17.5 % = .175
.175 * $70000 = $12250
$70000 - $12250 = $57750
How many types of triangles are there?
Answers
Answer:
there are 6 type of tryingle hope it helps
How many glasses of lemon juice and water are need to make 15 glasses of lemonade
A.14 glasses of lemon juice 1 glass of water
B.10 glasses of lemon juice 5 glasses of water
C.6 glasses of lemon juice 9 glasses of water
D.3 glasses of lemon juice 12 glasses of water
Answers
Answer:
Option B:10 glasses of lemon juice and 5 glasses of water
On a clear day you can see about 27 miles from the observation deck of the
Empire State Building in New York City. Using the formula below, estimate the
height in feet, h, of the observation deck. The distance, d, is in miles, and the
height, h, is in feet.
dava
A. 4.3 miles
B. 506 feet
C. 875 feet
D. 1050 feet
Answers
Larry deposits $1,500 in a savings account. How much interest would accrue after 10 years at a 2.5% rate?
Answers
Answer:
6000 dollar store for the day of a rectangle
Answer:
if its simple interest: $375 in interest, so he would have $1875 in total
if its compound interest: $420.13 in interest, so he would have $1920.13 in total
Step-by-step explanation:
I=Prt for simple interest, where I is interest, P is principle or the original amount, r is the interest rate, and t is the amount of time.
but compound interest adds on to the total instead of the initial savings so its more complicated
3 A(3, 1 1/2), B(- 5, - 3) and C(7, - 2) are the vertices of triangle ABC. What are the coordinates of M, the midpoint of BC and of Q, the midpoint of AM?
Answers
Un capital de S/. 42.000 colocado a una tasa de interés del 7% capitalizable anualmente, ¿en cuántos meses produce un interés de S/. 8 700?
Answers
Answer:
Se requiere 34 meses para producir un interés de 8700 soles.
Step-by-step explanation:
Asumamos que el capital aumenta conforme a una tasa de interés compuesto, cuya fórmula se describe aquí abajo:
[tex]C = C_{o}\cdot \left(1 + \frac{r}{100} \right)^{t}[/tex] (1)
Donde:
[tex]C_{o}[/tex] - Capital inicial, en soles.
[tex]C[/tex] - Capital actual, en soles.
[tex]r[/tex] - Tasa de interés mensual, en [tex]\frac{1}{a}[/tex].
[tex]t[/tex] - Período de capitalización, en años.
Si sabemos que [tex]C_{o} = 42000[/tex], [tex]C = 50700[/tex] y [tex]r = 7\,\frac{\%}{a}[/tex], entonces el período de capitalización es:
[tex]C = C_{o}\cdot \left(1 + \frac{r}{100} \right)^{t}[/tex]
[tex]\frac{C}{C_{o}} = \left(1 + \frac{r}{100}\right)^{t}[/tex]
[tex]\ln \frac{C}{C_{o}} = t\cdot \ln \left(1 + \frac{r}{100}\right)[/tex]
[tex]t = \frac{\ln C - \ln C_{o}}{\ln \left(1+\frac{r}{100} \right)}[/tex]
[tex]t = \frac{\ln 50700 - \ln 42000}{\ln \left(1+\frac{7}{100} \right)}[/tex]
[tex]t = 2.782\,yr[/tex]
Es decir, se requiere 34 meses para producir un interés de 8700 soles.
work out 37.56 divided by 12 and show working out
Answers
[tex]\longrightarrow{\green{3.13}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
[tex] \frac{37.56}{12} [/tex]
➺ [tex]\:3.13[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35\:ヅ}}}}⋆[/tex]
Answer:
3.13
Step-by-step explanation:
sorry that is All what I can say please don't be mad at me
Young people ages 15-24 are accountable for ____ of the total costs of motor vehicle injuries.
10%
20%
30%
40%
Answers
Answer:
30%
Step-by-step explanation:
The speed of an airplane is 1,240 km per hour. Find the distance covered by the airplane in
3 hours and 20 minutes. Also, express the distance in scientific notation.
Answers
Answer:
the answer is 4133.33...km
Explaination:
Distance = speed x time
Distance = 1240 x 10 / 3 = 4133.33... Km
Samantha earned $15 per hour. After a raise, she now earns $16.50 per hour. What is the percent increase of Samantha’s wages?
Answers
Answer:
1.5 percent I 5hink 9ook
Mrs. Santiago's consumer science class is making two different-size cheesecakes for
a fundraiser.
The large cheesecake has a diameter of 12 inches
The small cheesecake has a diameter of 4 inches
Part A: If the pans are both 3 inches deep, how many times greater is the volume
Of the large pan than that of the small pan? Show your work
Part B: When shipped, the large cheesecakes will be packaged in a box with dimensions of 12 in x
12 in x 3 in. What percentage of the box does the large cheesecake take up?
Show all work for each part and give at least 2 sentences explaination for each part.
Answers
Answer:
Part A: 9 times
Part B: 79%
Step-by-step explanation:
Part A:
Volume of the large pan = πr²h
Where,
radius (r) = ½(diameter) = ½(12) = 6 in.
height (h) = 3 in.
Volume = π*6²*3
Volume of the large pan = 339.29 in.³
Volume of the small pan = πr²h
r = ½(4) = 2 in.
h = 3 in
Volume of small pan = π*2²*3
Volume of the small pan = 37.7 in.³
✔️To determine how many times the volume of the large pan is greater than the small pan, divide the volume of the larger by the smaller:
= 339.29/37.7 ≈ 9
✅The volume of the large pan is about 9 times greater than the volume of the smaller pan.
Part B:
✔️Find the volume of the box:
Volume of box = L*W*H
Where,
L = 12 in.
W = 12 in.
H = 3 in.
Volume of the box = 12*12*3 = 432 in.³
Divide the volume of the large pan over the volume of the box and multiply by 100%
Thus:
339.29/432 × 100
= 78.5393519 ≈ 79%
The large cheesecake takes up about 79%
Given the functions f(x) = 2x – 1 Tand g(x) = 2x + 4, which operation results in the largest coefficient on the x term
Answers
Multiplication.
Step-by-step explanation:Given functions:
f(x) = 2x - 1
g(x) = 2x + 4
Let's perform some basic arithmetic operations on them to see which will result in the largest coefficient of the x term
i. Addition.
f(x) + g(x)
(2x - 1) + (2x + 4)
2x - 1 + 2x + 4
4x + 3
Here, the x term has a coefficient of 4
ii. Subtraction
f(x) - g(x)
(2x - 1) - (2x + 4)
2x - 1 - 2x - 4
-5
Here, the x term does not exist or has a coefficient of 0
iii. Multiplication.
f(x) * g(x)
(2x - 1) * (2x + 4)
4x² + 8x - 2x - 4
4x² + 6x - 4
Here, the x term has a coefficient of 6
iv. Division
Division is not exactly applicable here since there are not terms cancelling out.
Therefore, the multiplication operation will result in the largest coefficient on the x term with the coefficient being 6
The area of Ray’s rectangular living room, in square feet, can be found by using the expression 4(3x+3y). Use the distributive property to write an equivalent expression for the area of Ray’s living room. Equivalent Expression Use your equivalent expression to find the area of Ray’s living room, in square feet, if x = 2 and y = 4. Write answer here: square feet Show work
Answers
Answer:
Area = 72 square feet
Step-by-step explanation:
[tex]4(3x+3y)[/tex]
Multiply the four to the values inside the parentheses to find the "equivalent expression"
[tex]12x +12y[/tex]
Using the "equivalent expression" we found above, we now want to find the area of Ray's living room, in square feet if [tex]x=2[/tex] and [tex]y = 4[/tex]
[tex]12(2) + 12(4)[/tex]
[tex]= 24 +48[/tex]
[tex]= 72[/tex]
In a group of 33 pupils, 9 play the flute only.
8 play the piano only.
11 play neither instrument.
A student is selected at random.
What is the probability the student plays both instruments?
Answers
Answer:
ans: 5
Step-by-step explanation:
use the set theory to solve it,
Find the circumference of circle L. Write your answer as a decimal, rounded to the nearest hundredth.
Answers
I hope this answers your question and best of wishes!!
A furniture maker has two pieces of wood. One is 48 inches long, and the other is 64 inches long. The wood needs to be cut into pieces of equal length with no wood left over. What is the greatest possible length the furniture maker can cut each piece of wood?
A) 24 inches
B) 16 inches
C) 12 inches
D) 8 inches
Answers
Answer:
Step-by-step explanation:
16
Find the slope between (2, 10) and (9, 1). Substitute in the following numbers that are missing
Answers
Answer:
Rise (1-10)=-9
Run=(9-2)=7
Step-by-step explanation:
The slope is Rise/Run = -9/7
According to the Bureau of Labor Statistics, healthcare occupations is projected to grow from approximately 13.6 million jobs in 2018 to about 15.5 million jobs in 2028. Healthcare occupations are projected to add more jobs than any of the other occupational groups. This projected growth is mainly due to an aging population, leading to greater demand for healthcare services.
Answers
Answer:
The correct answer is "14%".
Step-by-step explanation:
Given:
Jobs in 2018,
= 13.6 million
Jobs in 2028,
= 15.5 million
Now,
In healthcare occupation, the projected percent increase will be:
= [tex]Increase \ in \ jobs\times \frac{100}{No. \ of \ jobs \ in 2018}[/tex]
By putting the values, we get
= [tex](15.5-13.6)\times \frac{100}{13.6}[/tex]
= [tex](1.9)\times \frac{100}{13.6}[/tex]
= [tex]13.97[/tex] (%)
or,
= [tex]14[/tex]%
Answer:
its 14
Step-by-step explanation:
i got it right
Write an equation of the parabola that passes through the point (46, - 150) and has x-intercepts - 4 and 56 . Then find the average rate of change from x= -4 to x=6.
An equation is y =
The average rate of change is
Answers
Answer:
6w83ywytahausjsshshfwgwyee
What's the equation? Week (w) 0 1 2 3 4 5 6 7 8 Infected (I) 1 2 4 8 16 32 64 128 256
Answers
Answer:
The Equation Is - Week(n) = [tex]2^{n}[/tex] (infected)
Step-by-step explanation:
Now We Have to just Put The Value Of 'n'.
Week(0) = 1
Week(1) = 2
Week(2) = 4
Week(3) = 8
Week(4) = 16
and so on.
write 12/16 as a fraction in simplest form . Then write the equivalent decimal and percent. Show your work.
simple form
decimal
Percent
Answers
Answer:
3/4, 0.75, 75%
Step-by-step explanation:
[tex]\frac{12}{16}[/tex]
divide top and bottom by 4
[tex]\frac{3}{4}[/tex]
The point (4, -8.5) is reflected across the y axis on a coordinate plane to create a new point. What is the distance between the two points in units.
Answers
Answer:
8units
Step-by-step explanation:
If the coordinate (x,y) is reflected over the y axis, the resulting coordinate will be (-x, y)
For the coordinate (4,-8.5), the resulting point after reflection will be (-4, -8.5)
Using the distance formula;
D = √(x₂-x₁)²+(y₂-y₁)²
D = √(-8.5+8.5)²)²+(-4-4)²
D =√(-8)²
D = √64
D = 8
Hence the required distance is 8units
what is the numeriacal value of 3x +2y -5xy when x=2 and y=3?
Answers
Answer:
- 30
Step-by-step explanation:
3x + 2y - 5xy
3(2) - 2(3) - 5((2)(3))
6 - 6 - 30
6 - 6 - 30
- 30
Juan is 5 and his mom is 35. In how many years will Juan's mom be 3 times Juan's age?
Answers
Juan will be 15 and his mom will be 45
15x3=45
Answer:
10 yrs
Step-by-step explanation:
Juan is 5 yrs now, mom is 35.
add 10 yrs to both the ages
juan is 15 and mom is 45
15 x 3=45
CAN SOMEONE HELP ME WITH THIS PLEASE AND THANK YOU.
Answers
Answer:
six and one over twelve
Step-by-step explanation:
1/4 + 5 5/6=1/4+35/6 = 6 1/12
step 3 35
6
step 4 answer = 35
6
1. Find the sum of the measures of the interior angles of a convex hexagon.
a. 900°
b. 1080°
c. 720°
d. 1440°
Answers
Answer:
could you include a pic please?