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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Answers
Answer:
(x^2-1)(x+1)=0
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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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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]
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From the attached tables,
[tex]g(5) = 2[/tex]
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Step-by-step explanation:
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Answers
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A die usually have 6 numbers so ill assume it has that.
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Alexis surveys a random sample of 80 students at his school and finds that 22 of them
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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
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Thus, the number of students who usually walk to school will be 484 students.
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Answer:
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Answer:
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Answer:
A. A boxplot of the data has multiple large outliers.
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B) YEs the mean and median of the normal distribution are nearly equal. AS it is asymmetrical.
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Answers
Answer:
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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:-
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Answers
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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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Answers
9514 1404 393
Answer:
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Step-by-step explanation:
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sin(α+β) = sin(α)cos(β) +cos(α)sin(β)
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Answer:
B) (-6,9)
Step-by-step explanation:
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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
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Step-by-step explanation:
15-8=7 green skateboards
3:7