Find the indicated limit, if it exists.
The limit is approaching 5.
Possible Options:
a) 0
b) 8
c) 3
d) The limit does not exist
Answers
Answer:
d) 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 [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 a limit to exist, the right-side and left-side limits must equal each other.
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}[/tex]
Step 2: Find Right-Side Limit
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 5^+} 5 - x[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 5^+} 5 - x = 5 - 5 = 0[/tex]Step 3: Find Left-Side Limit
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 5^-} x + 3[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 5^+} x + 3 = 5 + 3 = 8[/tex]∴ Since [tex]\displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)[/tex] , then [tex]\displaystyle \lim_{x \to 5} f(x) = DNE[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Related Questions
A fair die is rolled twice. What is the probability that each roll shows an odd number? (show work)
Answers
Answer:
1/4
Step-by-step explanation:
To find probability, multiply the probability of one roll times the probability of the second roll.
A die usually have 6 numbers so ill assume it has that.
1/2 or 3/6 of the sides are odd. So multiply 1/2*1/2 to get 1/4.
What’s the correct answer I will mark as brainlest ASAP
Answers
Answer:
9
Step-by-step explanation:
240x.70=168 left after 30% to teacher
168/2=84 left after putting half in jar
25 students x 3=75 given to students
84-75=9 left
Some1 hurry need help
Answers
Answer:
B) (-6,9)
Step-by-step explanation:
since it's reflecting on the x-axis, the x is gonna stay the same. the y changes though. opposite of -9 is 9.
hope this helps <3
Answer:
B, (-6, 9)
Step-by-step explanation:
this is because it's like as if it was a mirror, so that is the correct answer
x
Given the functions f and g in numerical (table ) forms as
-1 0 1 23 4
f(x)
x 1
2 5 5 3 4 3
g(x) 1
Compute: gof (1)
2
0
3
8
4
3
5
2
6
1
Done
Answers
Answer:
[tex]g\ o\ f(1) = 2[/tex]
Step-by-step explanation:
Given
The attached tables
Required
[tex]g\ o\ f(1)[/tex]
This is calculated as:
[tex]g\ o\ f(1) = g(f(1))[/tex]
From the attached tables,
[tex]f(1) = 5[/tex]
So, we have:
[tex]g\ o\ f(1) = g(5)[/tex]
From the attached tables,
[tex]g(5) = 2[/tex]
So, we have:
[tex]g\ o\ f(1) = 2[/tex]
hi please help! ill give u a good 5 starz :)
Answers
Answer:
Option C and D!
Step-by-step explanation:
Option C because:-When 9 is placed in the box after 7, we get:-
7 ÷ 9 = [tex]\frac{7}{9}[/tex] which is correct!
7 ÷ 9 can also be written as [tex]\frac{7}{9}[/tex]. So, this Option is right since the equation is correct when 9 is placed in the box!
Option D is also correct because,When we place 9 in the box before [tex]\frac{1}{9}[/tex], we get:-
9 ÷ [tex]\frac{1}{9}[/tex] = 81
9 ÷ [tex]\frac{1}{9}[/tex] equals 9 x 9 (take the reciprocal of [tex]\frac{1}{9}[/tex])
9 x 9 equals 81 which means the equation is correct when 9 is placed in the box!
URGENT NEED HELP CLICK TO SEE
Answers
Answer:
3:7
Step-by-step explanation:
15-8=7 green skateboards
3:7
please answer this as quick as possible.
Answers
Answer:
False
x=8-10=-2
Step-by-step explanation:
[tex]10 = x - 8 \\ ➡ \: x = 10 + 8 \\ ➡ \: x = 18[/tex]
[tex]\sf\red{The\:value\:of\:x\:is\:18.\:}[/tex]
[tex]\sf\pink{Hence,\:it\:is\:false.}[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and plans to construct a 95% confidence interval for the mean, using an SRS of 16 bags. Suppose he is not sure if the distribution of net weights is Normal. In which of the following circumstances would he not be safe to use a t procedure?
A. A boxplot of the data has multiple large outliers.
B. The mean and median of the data are nearly equal.
C. The sample standard deviation is large.
D. A boxplot of the data shows a very slight skew.
Answers
Answer:
A. A boxplot of the data has multiple large outliers.
D. A boxplot of the data shows a very slight skew.
Step-by-step explanation:
A) The normal distribution does not have outliers. The outliers are any point outside the 3σ interval which 99.7% of the data. The 0.3% data would not be outliers.
B) YEs the mean and median of the normal distribution are nearly equal. AS it is asymmetrical.
C) When the sample standard deviation is large the data is spread about the mean. The normal distribution is flatter and wider
D) The normal distribution is never skewed.If one end is longer then the distribution is not assymmetric and the normal distribution asymmetric meaning half is the mirror reflection of the other half.
So A and D indicate circumstances where he not be safe to use a t procedure.
Which of the following graphs is the graph of a linear function?
Answers
Answer:
A is the answer
Step-by-step explanation:
multiply 6kg25g by 8
Answers
48kg200g....…........
Answer:
(6*1000)g+25g=6025g
6025g*8=48200g
48kg200g. {:1000g=1kg}
Find the exact value of the following, without using a calculator.
Answers
9514 1404 393
Answer:
(√17 -4√595)/102
Step-by-step explanation:
To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.
sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle
cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6
sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle
cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17
The sum of angles formula is ...
sin(α+β) = sin(α)cos(β) +cos(α)sin(β)
So, our sine is ...
[tex]\sin\left(\sin^{-1}\left(\dfrac{1}{6}\right)+\tan^{-1}(-4)\right)=\dfrac{1}{6}\cdot\dfrac{1}{\sqrt{17}}+\dfrac{\sqrt{35}}{6}\cdot\dfrac{-4}{\sqrt{17}}\\\\=\dfrac{1-4\sqrt{35}}{6\sqrt{17}}=\boxed{\dfrac{\sqrt{17}-4\sqrt{595}}{102}}[/tex]
a house purchased for 170828 is worth $73828 after 12 years. assuming that the house's value depreciated the same amount from year to year, what was it worth at the end of the year 4? Round to the nearest cent.
Answers
Answer:
After four years the house was worth $128,891.03
Step-by-step explanation:
170828(x)^12 = 73828
solve for x
x = 0.932 (House depreciates by 6.8% yearly)
plug in x and change into function and substitute 4 for 12 because it's 4 years
170828(0.932)^4
128891.0334
Answer:
Match the packaging type with the number of seedlings it contains.
gerbera daisy cell pack
gerbera daisy flat
standard flat
standard cell pack
Step-by-step explanation:
Alexis surveys a random sample of 80 students at his school and finds that 22 of them
usually walk to school. There are 1,760 students at the school. Predict the number of
students who usually walk to school.
Answers
Answer:
484 students
Step-by-step explanation:
This is simple probability. Assuming 22/80 students walk to school within a small population, and there are 1760 students at the school, there should be (22/80)*1760 students that walk to school in total. (This is just theoretical). This is 484 students.
The number of students who usually walk to school will be 484 students.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Alexis surveys a random sample of 80 students at his school and finds that 22 of them usually walk to school.
Then the number of students who usually walk to school will be
⇒ 22 / 80
⇒ 11 / 40
We know that the ratio will remain the same.
There are 1,760 students at the school.
Let x be the number of students who usually walk to school.
Then the number of students who usually walk to school will be
x / 1760 = 11 / 40
x = 484 students
Thus, the number of students who usually walk to school will be 484 students.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
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Answers
answer:
15
step-by-step explanation:
9, 10, 15, 17, 15, 14, 37, 45, 42, 13
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Answers
Answer:
(x^2-1)(x+1)=0
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Step-by-step explanation:
Answer:
(x^2-1)(x+1)=0
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Step-by-step explanation:
Calvin wrote inequalities to compare the heights, in feet, of rivers above or below flood stage.
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Answers
Answer:
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Silas just bought a used car for $5000. It loses value at a rate of 30% per year. The value of the car in n years is modeled by the formula f(n)=5000*(0.70)^ n-1 . Approximately how much will the car be worth in 5 years?
Answers
Answer:
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Write your answer as a fraction in simplest form.
Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
Covering
two dimensional
unit squares
Step-by-step explanation:
Hope this helps! Sorry if incorrect
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SEE ATTACHED FILE.
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the amount of gas used by a household is shown in the table. what is the slope of the data from the table
Answers
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Step-by-step explanation:
How long will it take the skier to travel 360 meters? Explain how you figured it out.
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Step-by-step explanation:
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Mary has 37 sheep in her flock. If she makes one group of 7 sheep, how many equal groups of 3 sheep can be made with the remaining sheep?
Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
2 1/6 ft
Step-by-step explanation:
This problem bothers on subtraction of fraction
Given data
Total length of rope 3 1/2 feet
Let's convert mixed fraction to proper fraction = 7/2ft
First piece of rope = 1 1/3ft
= 4/3ft
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Second piece = 2 1/6 ft
I think