Answers
Answer:
The limit does not exist
General Formulas and Concepts:
Calculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Left-Side Limit: [tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Step-by-step explanation:
*Note:
In order for the limit to exist, the right-hand and left-hand limits must equal each other
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left \{ {{x + 10,\ x < 8} \atop {10 - x,\ x \geq 8}} \right.[/tex]
Step 2: Find Right-Hand Limit
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 8^+} 10 - x[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 8^+} 10 - x = 10 - 8 = 2[/tex]Step 3: Find Left-Hand Limit
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 8^-} x + 10[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 8^+} x + 10 = 8 + 10 = 18[/tex]∴ since [tex]\displaystyle \lim_{x \to 8^+} f(x) \neq \lim_{x \to 8^-} f(x)[/tex], [tex]\displaystyle \lim_{x \to 8} f(x) = DNE[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Related Questions
Gabe and Bridgette are preparing meals to serve at a local homeless shelter. The number of people they will be able to serve depends on the number of meals they prepare.
p = the number of people Gabe and Bridgette will be able to serve
m = the number of meals Gabe and Bridgette prepare
Which of the variables is independent and which is dependent?
Answers
Answer:
The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.
Step-by-step explanation:
In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.
Answer:
independent variable = m
dependent variable = p
Step-by-step explanation:
The number of people they are able to serve depends on the number of meals they prepare.
I don’t know I just need the answer
Answers
Joseph has a standard deck of 52 playing cards. What is the probability that Joseph will draw a Jack then a Queen with replacement?
Answers
Answer: four out of 52 to pull a jack
Step-by-step explanation:
6th grade math help me please and thank you
What should I do FIRST to solve this problem?
5f - 7 = 23
divide by 5 on each side
subtract 7 from each side
subtract 23 from each side
add 7 to each side
Answers
Answer:
add 7 to both sides
then you are left with 5f=30
divide by 5 on both sides
you get f=6
Step-by-step explanation:
Is Avogadro's number the same for all elements?
Answers
The Avogadro's number of every element remains is the same. The number of atoms of 1 mole in every element is Avogadro's number. One mole of an element is 6.02214076×10²³ atoms.
What is an atom?
Each atom is made up of a nucleus and one or more electrons that are linked to it. One or more protons and a significant number of neutrons make up the nucleus. Only the most prevalent type of hydrogen is neutron-free. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The number of atoms of one mole substance is 6.02214076 × 10²³ which is Avogadro's number.
To learn more about Avogadro's number, click on the below link:
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Find f(-2) for f(x) = 2 x 3x
O A. -18
O B. 2/9
O c. 1/18
O D. -36
Answers
Step-by-step explanation:
f(x) = 2 x 3x
2 x 3x
2 (-2) 3(-2)
-4-6=-10
Step-by-step explanation:
f(x)=2 x 3x
2 x 3x
2(-2) 3 (-2)
-4 - 6 = -10
7. The power of the expressions 2x is
Answers
Answer:
2x= 1
hope it is helpful to you
A box of cookies contains three chocolate chip cookies, two oatmeal raisins, and four
gingerbreads. What is the probability of picking a chocolate chip, and then a gingerbread?
Answers
Answer: [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
Given
A box contains 3 chocolate chip cookies, 2 oatmeal raisins, and 4 gingerbreads
First Probability of selecting a chocolate chip is
[tex]\Rightarrow \dfrac{3}{9}[/tex]
After that there are 8 items left. So probability of selecting a gingerbread
[tex]\Rightarrow \dfrac{4}{8}[/tex]
On combining, the required probability is
[tex]\Rightarrow \dfrac{3}{9}\times \dfrac{4}{8}\\\\\Rightarrow \dfrac{1}{6}[/tex]
Given both, find (f-g)(x)
Answers
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Functions.
Here, we are given with,
f(x) = 4x + 4 and g(x) = 5x - 8
hence, now we have time get (f-g) (x)
so we get as,
==> (f-g) (x) ==> f(x) - g(x)
===> 4x + 4 - (5x - 8)
==> 4x + 4 -5x +8
==> -x + 12
==> hence, 12 - x
so we get as,
(f-g) (x) ==> 12 - x
Rasheen and Eric went to Taco Express. Rasheen bought seven tacos and two fajitas and paid $12.65. Eric bought four tacos and one fajita and paid $6.95. Find the cost of one taco.
Question 8 options:
$1.35
$1.45
$1.25
$1.95
Answers
Explain: the taco is is for $1.25 and the fajitas 1.95
Rasheen: order 7tacos: 1.25x7= $8.75 , and 2 fajitas: 1.95x2= $3.9
8.75+3.9 = $12.65
A bag contains 8 red marbles, 6 blue marbles and 7 green marbles. If two marbles are
drawn out of the bag, what is the probability, to the nearest 1000th, that both
marbles drawn will be red?
Answers
Answer:.029
Step-by-step explanation:
The probability of the first being blue is 6/17, the second is 5/16 and the third is 4/15. Multiply these together to get the total probability:
6/17 x 5/16 x 4/15 = .029
ps: have a nice day :)
What is the slope of the line through the points (-8, 4) and (4,4)?
Answers
Answer:
0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-4)/(4-(-8))
m=0/(4+8)
m=0/12
m=0
Please help. Worth 30 points.
Answers
Answer:
y = -3x + 5)
Step-by-step explanation:
We see immediately that the line crosses the y-axis at (0, 7). The line also goes through (4, -5). As we move from the first to the second point, x increases by 4 and y decreases by 12. Thus, the slope of this line is m = -12/4, or m = - 3.
Using the slope-intercept form,
y = -3x + 5)
Answer: y=3x+7
Step-by-step explanation: You need to remember y=mx+b. M is the slope and b is the y intercept. The y intercept is easy as it's were the line touches the y axis or in this case 7. The slope is rise over run meaning you find a point on the graph like (2,1) and you count how many spaces up until your next to a point, and then you see how many spaces you have to move over or run. In this case you rise 3 and run 1 meaning the slope is [tex]\frac{3}{1}[/tex] or just 3.
What is the volume of a hemisphere with a radius of 3.8in, rounded to the nearest tenth of a cubic inch
Answers
Answer: [tex]114.9\ in.^3[/tex]
Step-by-step explanation:
Given
The radius of the hemisphere is [tex]r=3.8\ in.[/tex]
The volume of a hemisphere is given by
[tex]V=\dfrac{2}{3}\pi r^3[/tex]
Insert the value
[tex]V=\dfrac{2}{3}\pi \times (3.8)^3\\\\V=114.9\ in.^3[/tex]
Katy organised a wedding. Guests had to choose their meal from pasta , chicken or beef. 1/3 of the guests chose pasta. 5/12 of the guests chose chicken. 24 of the guests chose beef. How many guests were at the wedding ?
guys please help i’ll even give brainliest and give the correct answer not wrong ones
Answers
With the help of equations we can say that, the wedding had 96 attendees.
What is an equation ?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
x is the total number of wedding attendees.
1/3 of the attendees =1/3 who chose pasta=1/3x----1
Those who selected chicken =5/12x---2
24 people opted for meat.----3
adding 1,2,3
x = 96
learn more about equation click here:
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Which number will have the same result, when rounded to the nearest hundred or thousand? (3-5) A 1,049 B 1,118 and 5 C 1,179 D 2,149
Answers
Answer:
The answer is "Option A".
Step-by-step explanation:
In this question except for choice "A", all the value is not nearest about the hundred or thousand, that why the correct answer is "1,049".
Someone please help me with this algebra
Answers
second answer: 112
i just followed the formulas given on the key
also pls give brainliest
A rectangular prism and its dimensions are shown in the diagram.
26
6.5 in.
5 in.
7.5 in.
What is the total surface area of this prism in square inches?
Record your answer and fill in the bubbles on your answer document. Be sure to use the
correct place value.
Answers
Answer: 21
Step-by-step explanation: you add and subtract
Answer:
21
Step-by-step explanation:
108% of 75.5 is what number
Answers
Answer:
81.54
Step-by-step explanation:
% of a # = (% * #)/100
% = 108
# = 75.5
(108 * 75.5)/100
8,154/100
81.54
OR
% of a # = (%/100) * #
% = 108
# = 75.5
(108/100) * 75.5 = 1.08 * 75.5
81.54
Solve Similar Triangles (advanced)
Solve for X.
Answers
Given:
[tex]m\angle B=90^\circ, m\angle D=90^\circ, AB=6, BD=4, BC=2, DE=x[/tex].
To find:
The value of x.
Solution:
In triangles ABC and ADE,
[tex]\angle B\cong \angle D[/tex] (Right angles)
[tex]\angle A\cong \angle A[/tex] (Common angles)
[tex]\Delta ABC\sim \Delta ADE[/tex] (AA property of similarity)
We know that the corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{AB}{AD}=\dfrac{BC}{DE}[/tex]
[tex]\dfrac{6}{(6+4)}=\dfrac{2}{x}[/tex]
[tex]\dfrac{6}{10}=\dfrac{2}{x}[/tex]
[tex]\dfrac{3}{5}=\dfrac{2}{x}[/tex]
On cross multiplication, we get
[tex]3\times x=5\times 2[/tex]
[tex]3x=10[/tex]
[tex]x=\dfrac{10}{3}[/tex]
Therefore, the value of x is [tex]\dfrac{10}{3}[/tex] units.
PLEASE HELP ASAP! 55 POINTS Jackie wraps a sheet of paper tightly around a wax candle whose diameter is two inches, then cuts through them both with a sharp knife, making a 45° angle with the candle's axis. After unrolling the paper and laying it flat, Jackie sees the wavy curve formed by the cut edge, and wonders whether it can be described mathematically. Sketch this curve, then show that it is sinusoidal. It is very helpful to use radian measure to describe angles in this problem.
Answers
Step-by-step explanation: You can make a 90-degree angle and put a line threw the center of the angle for a 45-degree angle. Then you can erase 1 side of the angle that was making a 90-degree angle.
which answer? (multiple choice).
Answers
if A={1,2,3}, find the relation in A×S satisfying the condition x+y<5.
Answers
Answer: This is copied from the internet:
Step-by-step explanation:
Answer:
For function, every element of the domain must have a unique image in co-domain...
(A)Let us redefine each function as a set of ordered pairs
and see if they satisfy the above condition (A) of a function f1={(1,2),(2,3),(3,4)} ; (4,5) cannot be an ordered pair as 5 does not belong to co-domain , Thus the element 4 of domain does not have an image.
f2={(1,4),(2,3),(2,4),(3,2)(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
The uniqueness is violated as the elements have not one but many images.
f3={(2,1),(3,2),(3,1),(4,1),(4,2),(4,3)} Not a function as in f2 uniqueness is violated.
f4={(1,4),(2,3),(3,2)(4,1)} It is a function as each element has a unique image.
hellllllllllllllllpppppppppppppp
Answers
Answer:
32m^2
Step-by-step explanation:
which system of equations has only one solution
4x+2y=8 -4x-2y=3
Answers
Step by step
4x + 2y = 8
Arrange in y intercept form
2y = -4x + 8
Divide all by 2 to solve
y = -2x + 4
-4x -2y = 3
Arrange in y intercept form
2y = -4x -3
Divide all by 2 to solve
y = -2x -3/2
These equations have the same slope (2) with different y intercepts, so they are parallel lines. Parallel lines never intersect so there is no solution.
NO FILES AT ALL JUST HELP ME
Answers
Answer:
4/20
Step-by-step explanation:
You borrowed $59,000 for 2 years at 11% which was compounded annually. What
total will you pay back?
Answers
Answer:
$72693.9
Step-by-step explanation:
To get this answer you need to use the compound interest formula, which will be A=P(1+r/n)^n(t). P=59,000 r=11%=0.11 n=1 (annually) t=2 years. From there you should be able to figure the rest out and get the answer. Hope this helps!
A machine makes 12 articles in half an hour.
How many articles will it make in 6 hours?
Answers
Answer:
144
I wish you luck in your assignments.
Answer: 144 articles
Step-by-step explanation:
If it makes 12 in half-hour, then 24 in an hour because 12*2 is 24.
then 24*6=144.
i need this answered
Answers
Answer:
69 pi is your answer.
6 x 10 is 60
answer these question, please