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
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]
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Answers
Answer:
the answer is b. the segment has a length of 8 units vertical.
Step-by-step explanation:
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Answer:
False
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Step-by-step explanation:
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Answers
Answer:
(x^2-1)(x+1)=0
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x=1; x=-1
Step-by-step explanation:
Answer:
(x^2-1)(x+1)=0
(x+1)(x-1)(x+1)=0
x=1; x=-1
Step-by-step explanation:
Move words to the blanks to make the sentence true. HELPP ME FASTTT PLEASEEE
Answers
filling, three-dimensional, unit squares
I hope this helps ^^
Answer:
Covering
two dimensional
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Step-by-step explanation:
Hope this helps! Sorry if incorrect
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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What’s the correct answer I will mark as brainlest ASAP
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Answer:
9
Step-by-step explanation:
240x.70=168 left after 30% to teacher
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84-75=9 left
Which of the following graphs is the graph of a linear function?
Answers
Answer:
A is the answer
Step-by-step explanation:
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?
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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.
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So A and D indicate circumstances where he not be safe to use a t procedure.
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Answers
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Answer:
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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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Answers
Answer:
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Calvin wrote inequalities to compare the heights, in feet, of rivers above or below flood stage.
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Answer:
I'm not 100% sure but I think its B. 1> -18
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Answers
Answer:
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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.
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Answers
Answer:
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Step-by-step explanation:
In an aquarium, there are 6 large fish and 8 small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.
Answers
Answer:
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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!
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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.
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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
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
This problem bothers on subtraction of fraction
Given data
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I think
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Answers
answer:
15
step-by-step explanation:
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mode means the number that appears the mostin the set of numbers, 15 appears twice, which the others appears only onceURGENT NEED HELP CLICK TO SEE
Answers
Answer:
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Step-by-step explanation:
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How long will it take the skier to travel 360 meters? Explain how you figured it out.
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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:
$1200.50
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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
Answer: 10 groups
Step-by-step explanation:
Since we know she is making a group of 7 sheep, we can do 37-7 to get 30 sheep left
If she wants to find how many groups she can make we have to do 30/3 which gets us to 10 which is the number of groups she can do
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Answers
Answer:
Look at the image.
Step-by-step explanation:
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]