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
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Step-by-step explanation:
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Step-by-step explanation:
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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
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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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.
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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.
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Answer:
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Step-by-step explanation:
Find the exact value of the following, without using a calculator.
Answers
9514 1404 393
Answer:
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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.
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Answers
Answer:
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Step-by-step explanation:
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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:
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Step-by-step explanation:
This problem bothers on subtraction of fraction
Given data
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Let's convert mixed fraction to proper fraction = 7/2ft
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= 4/3ft
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Answers
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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answer:
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Step-by-step explanation:
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2
0
3
8
4
3
5
2
6
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Answers
Answer:
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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]
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So, we have:
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From the attached tables,
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Answers
Answer:
After four years the house was worth $128,891.03
Step-by-step explanation:
170828(x)^12 = 73828
solve for x
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plug in x and change into function and substitute 4 for 12 because it's 4 years
170828(0.932)^4
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Answer:
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Answer:
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Step-by-step explanation:
Answer:
(x^2-1)(x+1)=0
(x+1)(x-1)(x+1)=0
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Step-by-step explanation:
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Answers
48kg200g....…........
Answer:
(6*1000)g+25g=6025g
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Answer:
Look at the image.
Step-by-step explanation:
Calvin wrote inequalities to compare the heights, in feet, of rivers above or below flood stage.
Select all of the inequalities that are correct.
A. -10 > -9
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Answers
Answer:
I'm not 100% sure but I think its B. 1> -18
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:
2/7
Step-by-step explanation:
There are 14 fish and 4 of them are small, red ones.
P(small red fish) = 4/14 = 2/7