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Math2 Test with Answers, Exams of Mathematics

Yildiz Technical University Mathematics

Exam for Math2 Subject Including 43 questions with theirs answers and explanation in the end

Typology: Exams

2019/2020

Available from 03/01/2022

Fareed125 🇹🇷

10 documents

1 / 28

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TEST SAMPLE I

1. Let {𝑎𝑛} be a sequence defined by 𝑎1= 1 , 𝑎2= 2 and 𝑎𝑛= 𝑎𝑛−1 + 𝑎𝑛−2 𝑓𝑜𝑟 𝑛 ≥ 3.

If the limit 𝐿 = lim

𝑛→∞

𝑎𝑛+1

𝑎𝑛 existss, then what is L ?

a. b. c. d. e.

2. Which of the following is true for the character of the sequence (𝑎𝑛)= ( 2

√𝑛2+𝑛−𝑛) ?

a. Divergent

b. Converges to 0.

c. Converges to 2.

d. Converges to 3.

e. Converges to 4.

3. What is the sum of the series ∑𝑛+2

3𝑛+1

∞

𝑛=0 ?

a. b. c. d. e. Divergent

4. What is the largest convergent inverval of the power series ∑5𝑥𝑛

(𝑛+1)!

∞

𝑛=0 ?

a. b. c. d. e.

5. Which of the following is true for the character of the sequence (𝑎𝑛)= ( −3

𝑛−√𝑛2+𝑛) ?

a. Divergent

b. Converges to 0.

c. Converges to 2.

d. Converges to 4.

e. Converges to 6.

6. What is the sum of the series ∑𝑛+2

2𝑛+1

∞

𝑛=0 ?

a. Divergent b. b. c. d.

Partial preview of the text

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TEST SAMPLE I

1. Let {𝑎𝑛} be a sequence defined by 𝑎 1 = 1 , 𝑎 2 = 2 and 𝑎𝑛 = 𝑎𝑛−1 + 𝑎𝑛−2 𝑓𝑜𝑟 𝑛 ≥ 3.

If the limit 𝐿 = lim 𝑛→∞𝑎 𝑎𝑛+1𝑛 existss, then what is L?

a. b. c. d. e.

2. Which of the following is true for the character of the sequence (𝑎𝑛) = ( √𝑛 2 +𝑛−𝑛^2 )?

a. Divergent

b. Converges to 0.

c. Converges to 2.

d. Converges to 3.

e. Converges to 4.

3. What is the sum of the series ∑^ ∞𝑛=0 3 𝑛+2𝑛+1?

a. b. c. d. e. Divergent

4. What is the largest convergent inverval of the power series ∑ ∞𝑛=0 (𝑛+1)!5𝑥𝑛?

a. b. c. d. e.

5. Which of the following is true for the character of the sequence (𝑎𝑛) = ( 𝑛−√𝑛−3 2 +𝑛)?

a. Divergent

b. Converges to 0.

c. Converges to 2.

d. Converges to 4.

e. Converges to 6.

6. What is the sum of the series ∑ ∞𝑛=0 2 𝑛+2𝑛+1?

a. Divergent b. b. c. d.

7. What is the largest convergent inverval of the power series ∑^ ∞𝑛=0 (𝑛+2)!7𝑥𝑛+1?

a. b. c. d. e.

8. Determine that the following series are convergent absolutely/conditionally or divergent.

I. II. III.

a. I and II convergent absolutely ; III divergent

b. I convergent conditionally; II convergent absolutely; III divergent

c. I and II convergent absolutely ; III convergent conditionally

d. I divergent; II convergent absolutely; III convergent conditionally

e. I and III divergent; II convergent absolutely

9. Determine that the following series are convergent absolutely/conditionally or divergent.

I. II. III.

a. I convergent absolutely ; II divergent; III convergent conditionally

b. I and III convergent conditionally; II divergent

c. I and II convergent absolutely ; III convergent conditionally

d. I divergent; II convergent absolutely; III convergent conditionally

e. I and III divergent; II convergent absolutely

10. Determine the character of the following series.

I. II. III.

a. I divergent; II and III convergent b. I and II convergent; III divergent

c. I and III divergent ; II convergent d. I , II and III divergent e. I, II and III convergent

11. Determine the character of the following series.

I. II. III.

Which of the following gives the sum and the convergent interval of?

Which of the following gives the sum and the convergent interval of?

18.Which of the following series represents the function on the convergent interval ?

Which of the following is another parametric representation of the curve given by ?

e) There is no other representation.

Which of the following is another parametric representation of the curve given by ?

e) There is no other representation.

Which of the following is the representation of the points which provides the inequality

in polar coordinates?

Which of the following is the representation of the points which provides the inequality

in polar coordinates?

Which of the following integral gives the area lies outside of the circle , inside of the cardioid for?
Which of the following is the domain of the vector valued function ?
Which of the following is the domain of the vector valued function

Which of the following is the plane equation which is parallel to the vectors

and passing from the point?

Which of the following is the plane equation which is parallel to the vectors and passing from the point?
Which of the following is the angle between the velocity and the acceleration vectors of tthe

position vector at?

Which of the following is the angle between the velocity and the acceleration vectors of tthe

position vector at?

What is?
Which of the following statement(s) are true for?

I. It is defined for all

II. The limit at is 0.

III. It is continuous at.

Which of the following statement(s) are true for?

I. It is defined for all

II. The limit at is 0.

III. It is continuous at.

For which value of b>0, the radius of convergence of the power series will be?
For which value of b>0, the radius of convergence of the power series will be?
For the vector valued function defined by , which of the statement(s) are true?

I. Domain is II. It is continuous at t= III. It does not have limit at t= IV. It is discontinuous at t=

Math2 Test with Answers, Exams of Mathematics

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Partial preview of the text

Download Math2 Test with Answers and more Exams Mathematics in PDF only on Docsity!

TEST SAMPLE I

1. Let {𝑎𝑛} be a sequence defined by 𝑎 1 = 1 , 𝑎 2 = 2 and 𝑎𝑛 = 𝑎𝑛−1 + 𝑎𝑛−2 𝑓𝑜𝑟 𝑛 ≥ 3.

If the limit 𝐿 = lim 𝑛→∞𝑎 𝑎𝑛+1𝑛 existss, then what is L?

a. b. c. d. e.

2. Which of the following is true for the character of the sequence (𝑎𝑛) = ( √𝑛 2 +𝑛−𝑛^2 )?

a. Divergent

b. Converges to 0.

c. Converges to 2.

d. Converges to 3.

e. Converges to 4.

3. What is the sum of the series ∑^ ∞𝑛=0 3 𝑛+2𝑛+1?

a. b. c. d. e. Divergent

4. What is the largest convergent inverval of the power series ∑ ∞𝑛=0 (𝑛+1)!5𝑥𝑛?

a. b. c. d. e.

5. Which of the following is true for the character of the sequence (𝑎𝑛) = ( 𝑛−√𝑛−3 2 +𝑛)?

a. Divergent

b. Converges to 0.

c. Converges to 2.

d. Converges to 4.

e. Converges to 6.

6. What is the sum of the series ∑ ∞𝑛=0 2 𝑛+2𝑛+1?

a. Divergent b. b. c. d.

7. What is the largest convergent inverval of the power series ∑^ ∞𝑛=0 (𝑛+2)!7𝑥𝑛+1?

a. b. c. d. e.

8. Determine that the following series are convergent absolutely/conditionally or divergent.

I. II. III.

a. I and II convergent absolutely ; III divergent

b. I convergent conditionally; II convergent absolutely; III divergent

c. I and II convergent absolutely ; III convergent conditionally

d. I divergent; II convergent absolutely; III convergent conditionally

e. I and III divergent; II convergent absolutely

9. Determine that the following series are convergent absolutely/conditionally or divergent.

I. II. III.

a. I convergent absolutely ; II divergent; III convergent conditionally

b. I and III convergent conditionally; II divergent

c. I and II convergent absolutely ; III convergent conditionally

d. I divergent; II convergent absolutely; III convergent conditionally

e. I and III divergent; II convergent absolutely

10. Determine the character of the following series.

I. II. III.

a. I divergent; II and III convergent b. I and II convergent; III divergent

c. I and III divergent ; II convergent d. I , II and III divergent e. I, II and III convergent

11. Determine the character of the following series.

I. II. III.