Answers
The two-sided limit exists as long as the limits from either side also exist and are equal. So to compute the limit, you have to compute the one-sided limits,
[tex]\displaystyle\lim_{x\to0^-}f(x)[/tex]
[tex]\displaystyle\lim_{x\to0^+}f(x)[/tex]
f(x) has a different definition and thus different behavior as x approaches 0 depending on which direction x is approaching 0:
• When x approaches 0 from the left (or from below), you use the definition of f for x < 0, so
[tex]\displaystyle\lim_{x\to0^-}f(x) = \lim_{x\to0}(-x-2) = -2[/tex]
• When x approaches 0 from the right (or above), you use the other definition, so
[tex]\displaystyle\lim_{x\to0^+}f(x) = \lim_{x\to0} \left(\frac x2-2\right) = -2[/tex]
The limits from either side match, so the two-sided limit exists and is also -2.
Related Questions
Should you use Sine, Cosine, Tangent to solve the following problem
Answers
Answer:
tangent
Step-by-step explanation:
SOH( sin = opposite/hypotenuse)
CAH(cosine = adjacent/hypotenuse)
TOA(tan = opposite/adjacent)
you are trying to find x and the numbers given to you are opposite of x and adjacent to x. that means you need to use toa
We will use Tangent of the angle.
What is Tangent of the angle?In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
Given that, a right triangle, with perpendicular = x and an acute angle = 28° and base = 14
Since, we know that, tan α = opposite side / adjacent side
In other two trigonometric ratios, we need the length of hypotenuse, which is not given.
Hence, We will use the Tangent of the angle.
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Lena bought new inline skates for $44.99. The sales tax was $4.13. How much did Lena spend in all for her new inline skates?
Answers
Step-by-step explanation:
Mam nice drawing at your backside Mam nice drawing at your backside
Para reunir dinero para su gira de estudios , los alumnos de un curso deciden vender números de una rifa que se encuentran numeradas del 1 al 100 ¿Cual es la probabilidad de ganar en la rifa si se compran todos los numeros que sean multiplos de 3 o de 5?
Answers
Respuesta:
0.53
Explicación:
Para calcular la posibilidad del evento A: "ganar la rifa comprando todos los números múltiplos de 3 o 5", debemos usar la siguiente fórmula.
P(A) = casos favorables / casos posibles
Evaluemos primero todos los casos que son múltiplos de 3, entre 1 y 100: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99. En total son 33.
Ahora, evaluemos todos los casos que son múltiplos de 3, entre 1 y 100: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100. En total son 20.
El número total de casos favorables es 33 + 20 = 53.
El número de casos posibles es el total de números de 1 a 100, es decir 100.
Luego P(A) = 53/100 = 0.53.
SOMEONE PLS HELP ASAP DUE SOON PLS AND TY PLSSS I NEED HELP
Answers
Answer:
1.48
Step-by-step explanation:
Formula:
degrees × (π)/180
85 × (π)/180
85π/180
17/36π
1.483
Rounded to nudredths: 1.48
Answer:
1.48
Step-by-step explanation:
I need help please!!
Answers
The width of a rectangle room is 80 percent of its length. WHat is the area of the room?
Answers
Answer:
180 squared ft
Step-by-step explanation
80% = 80/100 = 40/50 = 4/5
L = 15
W= 4/5 of 15 = 12
Area = LxW
Area = 15x12 = 180 squared ft
The probability that a person cannot read is 0.85 what is the probability that 2 people selected at random will be unable to read
Answers
Answer: 0.7225
Step-by-step explanation:
Since the probability that a person cannot read is 0.85. The probability that 2 people selected at random will be unable to read will be gotten by multiplying the value of the probability given twice. This will be
= P(not read) × P(not read)
= 0.85 × 0.85
= 0.7225
Therefore, the probability that 2 people selected at random will be unable to read is 0.7225
Can someone please help me with this
Answers
Answer:
[tex]2x^2+x+7y[/tex]
Step-by-step explanation:
We are given the equation [tex]2(x^2+3y)+x+y[/tex] and are asked to simplify it.
To do so, we need to first get rid of the parenthesis, since x² and 3y aren't like terms, it isn't solvable unless we try another way, which is the distributive property.
2 is next to the parenthesis, in the distributive property, we would multiply the number outside of the parenthesis with all the numbers inside the parenthesis. Therefore :
[tex](2*x^2) + (2*3y) + x +y[/tex]
[tex]2x^2 +6y+x+y[/tex]
Now that we have like terms, we can add them together :
[tex]2x^2 + 6y+x+y[/tex]
[tex]2x^2 + x+7y[/tex]
Answer:
Hello! Your answer would be, 2[tex]x^{2}[/tex] + [tex]x[/tex] [tex]7y[/tex]
Step-by-step explanation:
Hope I helped! Brainiest plz!♥ Have a nice morning! Hope you make a 100%! -Amelia
Is y=(x-6) 2 to the second power linear fraction or nonlinear fraction
Answers
Answer:
Non - linear as for it is not a straight line.
Step-by-step explanation:
To the second power it would make a curve not straight line.
Answer:
Do you mean y = (x-6)^2? If yes, it is NONLINEAR FRACTION
Step-by-step explanation:
If you graph it, it forms a parabola so it is considered as nonlinear fraction/function
What was his mistake????
Answers
Explain how to solve this.
Answers
Answer:
c=74
Step-by-step explanation:
48+58=106
180-106=74
Answer:
D is 122 A is 58 B is 48 C is 74
Step-by-step explanation:
A broker charges 70 per square foot to install windows how much does it cost to install the windows shown
Answers
Hey can yall help me
what's 9+10+2=
Answers
Answer:
21
Step-by-step explanation:
: P
Answer:
21
Step-by-step explanation:
umm that's kindergarten math-
Adealer gained a 10% profit by selling an article for birr 330.00 .What was the original price of the article
Answers
Answer:
$297
Step-by-step explanation:
Given data
Percent profit=10%
sales price= $330
% profit= (sales price-cost price)/sales price* 100
let the cost price be x
Substitute
10= (330-x)/330* 100
cross multiply
10= (33000-100x)/330
10*330= 33000-100x
3300=33000-100x
3300-33000=-100x
-29700=-100x
29700=100x
x=29700/100
x=297
Hence the cost price is
cost price=$297
3x + 4 = 5x -10 true or false this equation can be simplified combining like terms to become 8x + 4= -10
Answers
Need help please urgent. Correct answers only no links.
Answers
Answer:
the exact answer is 314.159265359
Step-by-step explanation:
but it simplifies to 314.16
Is 4.53 a real number?
yes or no
Answers
Answer:
yur
Step-by-step explanation:
Answer:
yeah it's a decimal so yes
PLEASE HELP 25 PLUS POINTS!!!THIS IS REALLY IMPORTANT
Answers
Answer: A- 12.5 million
Step-by-step explanation: all you have to do is 125% of 10 million and you get 12.5 million.
Answer:
40 million
Step-by-step explanation:
125% of x
125/100 * x = 1.25x
x+ 10 = 1.25x
(subtract x from both sides)
10 = 1.25x - x
10 = 0.25x
(divide both sides by 0.25)
10/0.25 = x
x= 40
Which goes to this inequality x + 1 < 3
Answers
Look at the image for more information
For the equation 3(7 + x) = 3x + k, what value of k will create an equation with no solutions?
Answers
Brody deposited $500 into a savings account that earns 2.1% simple interest. What is the total amount in his account after 7 years?
Answers
Answer:
73.5
Step-by-step explanation:
Part/whole=percent/100
?/500=2.1%/100
500 divided by 100 is 5, so 2.1% times 5 is 10.5, which is the amount of interest made per year.
So, 10.5 times 7 is 73.5
5. THINK SMARTER There are 246 children at
Debbie's school. There are 328 children
at Jacob's school. Without adding, explain
how you could estimate the number of
children at the two schools.
Answers
Answer:u can estimate 246 to 200 and u can estimate 328 to 300
Step-by-step explanation:
add 34
Of the fifth graders in oak elementary, 6/8 are in band. What fraction of the fifth graders are not in band?
Answers
explanation: because 6/8 plus 2/8 = 8/8
Answer:
2/8 of the fifth graders are not in band
Step-by-step explanation:
To find how many fifth graders are not in band, subtract the # of fifth graders in band. Your difference is the amount of fifth graders that are not in band. To check your answer add 2/8 + 6/8 which should be equal to 8/8 or a whole ( 1 ).
Line d is parallel to line c in the figure below.
Parallel lines d and c are intersected by lines q and p to form 2 triangles. At lines d and p, the angle is 2, at d and q, the angle is 1, and at q and p the angle is 3. At lines c and q, the angle is 4, at p and c, the angle is 5, and the third angle is 6.
Which statements about the figure are true? Select three options.
Vertical angles prove that Angle 2 is congruent to angle 5.
In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.
Vertical angles prove that Angle 3 is congruent to angle 6.
The triangles are similar because alternate interior angles are congruent.
In the two similar triangles, Angle 2 and Angle 4 are corresponding angles.
The triangles are similar because corresponding sides are congruent.
Answers
Answer: In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.
Vertical angles prove that Angle 3 is congruent to angle 6.
The triangles are similar because alternate interior angles are congruent.
Step-by-step explanation:
The height of a seat on a Ferris wheel can be modeled as
H (t) = 47 sin (Fot+ 3 + 52, where tis time in seconds and h(t) is
height in feet.
How far off the ground is a seat when it is at the top of the Ferris wheel?
A. 99 feet
B. 94 feet
C. 104 feet
D. 52 feet
Answers
Answer:
Step-by-step explanation:
Its 99
I just took it
the width of a rectangle is 2 inches less than its length, and the area is 35 sq inches. what are the length and width of the rectangle?
Answers
Answer:
5 and 7
Step-by-step explanation:
A swimming pool is in the shape of a right triangle. One leg has a length of 15 feet and the hypotenuse is √325 feet. Estimate the length of the other leg. Round to the nearest integer, if necessary
Answers
Answer:
10 feet
Step-by-step explanation:
a^2+b^2=c^2
15^2+B^2=365
225+b^2=365
b^2=100
b=10
Select all the expressions that are equivalent to 20% of 150.
Answers
Answer:
2 and 3
Step-by-step explanation:
30 is 20% of 150
I hope this helps
Have a great day
Which equation matches the function shown in the graph?
A. y=2sin(1/2x)+1
B. y=3sin(2x)
C. y=2sin(2x)+1
D. y=3sin(1/2x)
Answers
Answer:
the answer is A. y=2sin(1/2x)+1
Step-by-step explanation:
I input all four functions on desmos (a graphing calculator), and saw that A. y=2sin(1/2x)+1 was similar to the function shown in the graph
The function that matches the graph is y= 2 sin(1/2x) +1.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given:
let y = A sin ([tex]\omega[/tex]x + Ф)+ k
T= 4π, w= 2π/T = 1/2
Now, midline= 1/2( max + min)
=1/2(3-1)= 2/2
k=1
and, A= 3-1 = 2
So, y= 2 sin(1/2x + Ф) +1
as, Ф=0
So, y= 2 sin(1/2x) +1
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Combine these radicals
3V2-5V2
Plz help
Will give Brainlyest
Answers
Answer:
b
Step-by-step explanation:
because i said so and because i am tired and tired and tired
Answer:
[tex] - 2 \sqrt{2} [/tex]
Step-by-step explanation:
Subtract 5√2 from 3√2.
[tex] - 2 \sqrt{2} [/tex]
Hence, the answer is Option A. in decimal form the answer will be −2.82842712.
