Does this limit exist? Show steps
Answer:
Yes, the limit does exist.
Step-by-step explanation:
By definition, a limit in the form:
[tex]\displaystyle \lim_{x\to a}f(x)[/tex]
Exists if and only if:
[tex]\displaystyle \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)[/tex]
We are given the limit:
[tex]\displaystyle \lim_{x\to 2}\frac{x^2+x-6}{x^2-4}[/tex]
So, in order to prove that this limit exists, we simply have to show that:
[tex]\displaystyle \lim_{x\to 2^-}\frac{x^2+x-6}{x^2-4}=\displaystyle \lim_{x\to 2^+}\frac{x^2+x-6}{x^2-4}[/tex]
Let's do the left-hand side first. We can factor the function:
[tex]=\displaystyle \lim_{x\to 2^-}\frac{(x+3)(x-2)}{(x+2)(x-2)}[/tex]
Simplify:
[tex]\displaystyle =\lim_{x\to 2^-}\frac{x+3}{x+2}[/tex]
By direct substitution:
[tex]\displaystyle =\frac{(2)+3}{(2)+2}=\frac{5}{4}[/tex]
Now, we can evaluate the right-hand side. Again, factor:
[tex]=\displaystyle \lim_{x\to 2^+}\frac{(x+3)(x-2)}{(x+2)(x-2)}[/tex]
Simplify:
[tex]\displaystyle =\lim_{x\to 2^+}\frac{x+3}{x+2}[/tex]
And by direct substitution:
[tex]\displaystyle =\frac{(2)+3}{(2)+2}=\frac{5}{4}[/tex]
Since both the left- and right-hand limits equal 5/4, our original limit does indeed exist.
What is the length of the segment connection the points that have the coordinates (-9, 8) and (2, -5) A √130 B √218 C √290 D √338
Answer:
Step-by-step explanation:
How much wrapping is needed for a package that is shaped like a cube
16 in. on each edge?
Answer:
1536 in^2
Step-by-step explanation:
This is basically asking for the surface area so knowing that is a cube all the sides are equal so one side would be 16(16) which is 256 in ^2. The knowing that there is 6 sides you would multiply it by 6 which is 256(6)= 1536^2
Which is equivalent to 3x-4y=8
Answer:
The answer is D) Y = 3/4x-2
Step by step explanation:
3x - 4y = 8
Express it in the term of y.
Subtract 3x from both sides:
3x - 4y - 3x = 8 - 3x
- 4y = 8 - 3x
Divide both sides by -4
-4y/-4 = (8 - 3x)-4
y = 8/-4 - 3x/-4
y = -2 - (-3/4x)
y = -2 + 3/4x
y = 3/4x - 2
Question 6
5 pts
What is the distance between two points with coordinates at (-3, 15) and (12, -1)?
16.3
18.4
21.9
025
It takes 24 hours to drive from town A to town B. At an average speed of 31 mph, how far is it?
Answer:
744 miles
Step-by-step explanation:
each hour is 31 miles
the drive is 24 hours
31*24=744
Answer:
744 miles
Step-by-step explanation:
Dr. Kershaw Invests $25,000. She earns 10.0% simple annual interest on her investment. How
much more interest would Dr. Kershaw earn after 2 years if her investment had earned 10.0%
annual interest compounded annually?
A $5,000
B $0
C $5,250
D $250
i
Answer:
It should be C.
Step-by-step explanation:
I hope this helps
2 A motorist drove 162 miles in 3 hours. At that rate, how many miles would the motorist travel in a half hour? F 81 mi G 324 mi H 27 mi J 54 mi
can someone please help me ?
Answer:
i really dont know
Step-by-step explanation:
i really dont know
Answer:
27
Step-by-step explanation:
162 divide by 3 = 54 divided by 2 =27 I think this is the answer
Julisha poured 0.9 liter of water into an
empty flask. She boiled the water for 15
minutes then measured the amount of water
that remained. She found that 80% of the
water remained in the flask. Measured in
liters, how much water evaporated?
PLS I NEED HELP! ASAP.
Answer:
0.18
Rounded
0.2
Step-by-step explanation:
In the box below, enter the value that is missing from the table.
170 is the answer
Given ,
520 = 0
.°.
420 = 520-100
320 = 520-200
?= 520-350 = 1700 = 520-520
Mark the relation
f(0)=520f(100)=520-100=420f(200)=520-200=320Similarly
f(350)=520-350=170What is the magnitude of -10 + 24i?
Answer:
The magnitude of the complex number is 26.
Step-by-step explanation:
Magnitude of a complex number:
The magnitude of a complex number in the format of a + bi is:
[tex]\sqrt{a^2 + b^2}[/tex]
What is the magnitude of -10 + 24i?
a = -10, b = 24. So
[tex]\sqrt{(-10)^2 +(24)^2} = \sqrt{100+576} = \sqrt{676} = 26[/tex]
The magnitude of the complex number is 26.
Please help! I need to work out the size of angle x.
Answer:
50+x=120°{ sum of interior angle of a triangle is equal to the exterior opposite angle of a trianglex=120-50x=70°hope it helps.
Step-by-step explanation:
50 + x =120
x = 120 -50
x = 70
please help me to find this out i really really need help.
The diagram shows a triangular prism ABCDEF with a horizontal base ABEF.
Give your answer correct to 3 significant figures.
Answer:
38.7°
Step-by-step explanation:
Let the angle we're looking for be called x.
Consider ΔADF (which consists of sides AD, FD and FA, and which contains the angle x.
tan(angle)=opposite/adjacent
tan(x)=FD/FA
x=tan⁻¹(12/15)=38.6598082541°≈38.7°
Therefore, the length of the angle be [tex]x=38.65[/tex] degree.
What is the trigonometry?
Trigonometry states that the trigo mean 'triangle', and metry means métron is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given that,
Let the length of the angle be [tex]x[/tex].
Consider Δ[tex]ADF[/tex]
which consists of sides [tex]AD, FD[/tex] and [tex]FA[/tex], and which contains the angle [tex]x[/tex].
So,
tan(x)=Perpendicular / Base
i.e.,
[tex]tan(x)=\frac{FD}{FA}\\\\tan(x)=\frac{FD}{FA}\\\\x=tan^{-1}(\frac{12}{15})\\\\x=38.65[/tex]
Hence, the length of the angle be [tex]x=38.65[/tex] degree.
To know more about the trigonometry
https://brainly.com/question/27269972
#SPJ2
Diego predicts that his basketball teams has a 2/3 probability of winning each of their next 9 games.
PART A
Which is the most likely outcome for Diego's first game?
A
His team will win.
B
His team will lose.
C
His team will tie.
D
PART B
Why?
Answer:
g
Step-by-step explanation:
A 10 foot ladder is leaning against a house. The base of the ladder is 4 feet from the house. How far does the ladder reach up the house?
Answer:
9.17 feet
Step-by-step explanation:
Use the Pythogoras theorem, a^2 + b^2 = c^2
you are give c and b ( because one side is slanted, so c) so rearrange to get
c^2-b^2 = a^2
10^2 - 4^2 = 84
square root 84 to get
9.16515
Find the limit, if it exists. lim (x^3 -3x^2 +3)
Answer:
-1
Step-by-step explanation:
Assuming problem is: x->2 (x^3 -3x^2 +3)
Since the expression is continuous at x=2,
then the limit can be found just by evaluating the expression at x=2.
2^3-3(2)^2+3
8-3(4)+3
8-12+3
-4+3
-1
What is the answer? Thank you!
Maria, an experienced shipping clerk, can fill a certain order in 11 hours. Felipe, a new clerk, needs 13 hours to do the
same job. Working together, how long will it take them to fill the order?
Answer:Maria rate = 1/13 job/hr
-----
Felipe rate = 1/16 job/hr
----
Together rate = 1/x job/h
Step-by-step explanation: rate + rate = Together rate
1/13 + 1/16 = 1/x
----
16x + 13x = 13*16
------
29x = 13*16
x = 7.17 hrs = 7 hr 10 min 12 seconds (time to do the job together)
-------------
Cheers,
Rubberduck100000.
Find the volume. Round to the nearest tenth if necessary.
Answer:
120
Step-by-step explanation:
Since you have to find volume you have to multiply all the numbers.
So, 4*5*6 = 120
Answer:
120cm2
Step-by-step explanation:
Volume= length times width times the height. So.. 6×5×4= 120cm2 (btw the 2 means squared)
Not sure if this is the answer?
Answer:
x = 16
Step-by-step explanation:
Based in the tangent-secant theorem, we have the following equation showing the relationship between the secant and the tangent:
(2 + x)*2 = 6²
4 + 2x = 36
Subtract 4 from both sides
2x = 36 - 4
2x = 32
Divide both sides
2x/2 = 32/2
x = 16
The total number of running yards in a football game was less than 100. The inequality x < 100 represents the situation.
Which graph represents the inequality?
95 96 97 98 99 100 101 102 103 104 105
O,
95 96 97 98 99 100 101 102103104105
o
95 96 97 98 99 100101102103104105
95 96 97 98 99 100 101 102103104105
Answer:
sorry I'm late but it's b I'm on unit test on edge
Answer: it is b
Step-by-step explanation:
Suzanne collected data on the weight of her classmates. She found that the range of the data she collected was 17
Which of the following BEST explains what a range of 17 indicates?
A
The average distance of each point from the mean is 17.
.
B
The distance between the minimum and the maximum is 17.
С
The distance between the lower quartile to the upper quartile is 17.
D
The distance between the mean and the median in a skewed data set is 17
Answer:
the answer is A.
Step-by-step explanation:
a light bulb consumes 960 watt- hours per day. How many watt-hours does it consume in 5 days and 12 hours?
Find the area of the figure
Answer:
The answer should be 63.
Step-by-step explanation:
I'm not really sure because in order to find the area of the figure, you have to find the length of one of the sides and then multiply this by itself to find the area. I wouldn't be the first person to trust so for someone else to answer.
Answer:
[tex]base = \sqrt{ {9}^{2} - {8}^{2} } = \sqrt{17} \: in\\ area = area \: of \: triangle \: + \: area \: of \: trapezium \\ area = ( \frac{1}{2} \times base \times height) + ( \frac{1}{2} \times height(a + b)) \\ area =( \frac{1}{2} \times \sqrt{17} \times 8) + ( \frac{1}{2} \times 8 \times ((7 - \sqrt{17} ) + 7) \\area = 56 \: sq \: inches[/tex]
Find the area of this circle. Use 3 for .
A = 7r2
10 ft
[?] ft2
Answer:
300ft^2
Step-by-step explanation:
pi*r^2
pi*10^2
pi*100
3*100
300
Answer:
Step-by-step explanation:
3*[tex]5^{2}[/tex] = 75
i need to simplify this −x<−29
Answer:
x > 29
Step-by-step explanation:
Answer:
[tex]x > 29[/tex]
Step-by-step explanation:
Given: −x<−29
To find: Simplified
Solution: Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
The process entails collecting like terms, which implies adding or subtracting terms in an expression.
Multiply both sides by -1 (reverse the inequality)
[tex](-x) (-1) > (-29) (-1)[/tex]
Simplify
[tex]x > 29[/tex]
3(y+2/5)=−1/5
Solve for y
Answer:
y = -7/3 or -2.333
Step-by-step explanation:
3(y+2 / 5) = -1/5 ------- First you need to do what is outside of the paranthesis which is 3, so divide both sides by 3.
(y + 2 / 5) = -1/15 ------- Next, you multiply both sides by 5 given the denominator is 5 on the left side.
y + 2 = -1/3 -------- Now you just subtract 2 from both sides.
y = - 7 /3 ---------- Answer
What is the domain of the square root function graphed below? On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3). x less-than-or-equal-to negative 1 x greater-than-or-equal-to negative 1 x less-than-or-equal-to 0 x greater-than-or-equal-to 0
Answer:
Its D
Step-by-step explanation:
Ed2021
Answer
x greater-than-or-equal-to 0
Step-by-step explanation:
yes
The following box plot shows the number of years during which 40 schools have participated in an interschool swimming meet:
A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years.
At least how many schools have participated for more than 1 year and less than 6 years?
4 schools
8 schools
10 schools
20 schools
Answer:
20 schools is your answer
Have a good day
Answer:
20 is ur answer!
Step-by-step explanation:
I took the test and got it right, also credit goes to the other guy! Have a good day/night! <3
roberts middle school took 210 students on a school picnic at the picnic 60 students played vollyball what fraction of the students played vollyball at the picnic
Answer:
I could be wrong but it's 2/7 (i think)
Step-by-step explanation:
I hope this helps :)