Calculus 101 Final Exam

1. .

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

2. .

4/5

1/2

7/3

0

The answer is 4/5 because when you multiply the fractions 4/5, 1/2, and 7/3 together, you get 28/30. However, 28/30 can be simplified to 14/15, which is equivalent to 4/5. Therefore, 4/5 is the correct answer.

Explanation

The answer is 4/5 because when you multiply the fractions 4/5, 1/2, and 7/3 together, you get 28/30. However, 28/30 can be simplified to 14/15, which is equivalent to 4/5. Therefore, 4/5 is the correct answer.

3. .

5

-5

6

-6

not-available-via-ai

Explanation

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4. .

A

B

C

None of the following

not-available-via-ai

Explanation

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5. .

1/2

1

2

0

not-available-via-ai

Explanation

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6. .

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

7. .

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

8. .

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

9. .

E

-e

1/e

-1/e

The given options represent different values of the exponential function with base e. The correct answer is e because it is the value of e raised to the power of 1, which is the definition of the exponential function.

Explanation

The given options represent different values of the exponential function with base e. The correct answer is e because it is the value of e raised to the power of 1, which is the definition of the exponential function.

10. .

1

0

2

Does Not Exist

The given answer "0" is correct because the numbers "1", "0", and "2" are listed vertically, indicating that they are separate numbers. The phrase "Does Not Exist" is most likely referring to the answer choice "Does Not Exist" rather than being a part of the sequence. Therefore, the correct answer is "0".

Explanation

The given answer "0" is correct because the numbers "1", "0", and "2" are listed vertically, indicating that they are separate numbers. The phrase "Does Not Exist" is most likely referring to the answer choice "Does Not Exist" rather than being a part of the sequence. Therefore, the correct answer is "0".

11. .

[0,2]

R-{1}

[0,1]U(1,2]

[-19,1)

The correct answer is [0,1]U(1,2]. This answer represents the union of the intervals [0,1] and (1,2], which means it includes all numbers from 0 to 1 (including 0 and 1) as well as all numbers from 1 to 2 (excluding 1). Therefore, the answer is a combination of two intervals that cover the range from 0 to 2, with the exception of the number 1.

Explanation

The correct answer is [0,1]U(1,2]. This answer represents the union of the intervals [0,1] and (1,2], which means it includes all numbers from 0 to 1 (including 0 and 1) as well as all numbers from 1 to 2 (excluding 1). Therefore, the answer is a combination of two intervals that cover the range from 0 to 2, with the exception of the number 1.

12. .

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

13. .

A

B

C

D

not-available-via-ai

Explanation

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14. .

-9

-3

21

2

The given sequence is -9, -3, 21, 2. This sequence seems to follow a pattern where each number is obtained by multiplying the previous number by -3. Starting with -9, we multiply it by -3 to get -27, then multiply -27 by -3 to get 81, and finally multiply 81 by -3 to get -243. However, the next number in the sequence is 2, which breaks the pattern. Therefore, it is likely that there is an error or inconsistency in the sequence, and the given answer of -9 may not be correct.

Explanation

The given sequence is -9, -3, 21, 2. This sequence seems to follow a pattern where each number is obtained by multiplying the previous number by -3. Starting with -9, we multiply it by -3 to get -27, then multiply -27 by -3 to get 81, and finally multiply 81 by -3 to get -243. However, the next number in the sequence is 2, which breaks the pattern. Therefore, it is likely that there is an error or inconsistency in the sequence, and the given answer of -9 may not be correct.

15. .

-3

0

-1

3

The given sequence of numbers is -3, 0, -1, 3. The correct answer is -3. This is because it is the first number in the sequence.

Explanation

The given sequence of numbers is -3, 0, -1, 3. The correct answer is -3. This is because it is the first number in the sequence.

16. .

{-2,-1,1,2,4}

{-2,-1,2,4}

{-1,1,2}

{-1,2}

The answer {-1,2} is the only set that is present in all the given sets. It is the intersection of all the sets. The other sets either have additional elements or are missing elements that are present in the answer set. Therefore, {-1,2} is the correct answer.

Explanation

The answer {-1,2} is the only set that is present in all the given sets. It is the intersection of all the sets. The other sets either have additional elements or are missing elements that are present in the answer set. Therefore, {-1,2} is the correct answer.

17. .

E

1/e

1

0

The given expression is 1/e. The value of e is approximately 2.71828, which is a mathematical constant representing the base of the natural logarithm. Therefore, 1/e is equal to approximately 0.36788.

Explanation

The given expression is 1/e. The value of e is approximately 2.71828, which is a mathematical constant representing the base of the natural logarithm. Therefore, 1/e is equal to approximately 0.36788.

18. .

A

B

C

D

not-available-via-ai

Explanation

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19. .

(1,0)

(0,0)

Option 3

Option 4

The answer (0,0) is the correct choice because it is the only point that is given in the question. The other point (1,0) is not mentioned in the given options. Therefore, (0,0) is the only valid answer based on the information provided.

Explanation

The answer (0,0) is the correct choice because it is the only point that is given in the question. The other point (1,0) is not mentioned in the given options. Therefore, (0,0) is the only valid answer based on the information provided.

20. .

X=0

X=2

X=-1

X=-1,2

The given answer X=2 indicates that the value of X is equal to 2. This means that when the equation or problem is solved, the variable X is found to have a value of 2.

Explanation

The given answer X=2 indicates that the value of X is equal to 2. This means that when the equation or problem is solved, the variable X is found to have a value of 2.