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Math 132, Spring 2011 - Exam 2: Integration and Approximation Questions, Exams of Calculus

Dr. Bhim Rao Ambedkar University Calculus

The spring 2011 exam 2 for math 132, which covers topics related to integration and approximation. The exam consists of sixteen questions, including multiple choice questions and two written answer questions. The multiple choice questions are worth five points each, and there is no partial credit. The written answer questions are worth fifteen points each and may receive partial credit. Students are required to write their name and id number on the pages with written answers to receive one point for each question. Questions on the trapezoidal rule, simpson's rule, definite integrals, and finding areas and volumes.

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Math 132, Spring 2011 - Exam 2

NAME:

STUDENT ID NUMBER:

This exam contains sixteen questions. The first fourteen

are multiple choice questions and count for five points

each. There is no partial credit on these questions, so

read each question carefully, check your arithmetic

and make sure that you have marked the answer you in-

tended to mark. The last two questions, which are each

worth fifteen points, require written answers, and some

partial credit might be given. However, no credit will be

given for information that is not germane to the problem

at hand. Please make sure to write your name and stu-

dent ID number on the pages that include your answers

to the last two questions. In fact, you will get one

point on each of these two questions for writing

your name and ID number legibly.

Discover Exams of Calculus Dr. Bhim Rao Ambedkar University

Partial preview of the text

Download Math 132, Spring 2011 - Exam 2: Integration and Approximation Questions and more Exams Calculus in PDF only on Docsity!

Math 132, Spring 2011 - Exam 2

NAME:

STUDENT ID NUMBER:

This exam contains sixteen questions. The first fourteen are multiple choice questions and count for five points each. There is no partial credit on these questions, so read each question carefully, check your arithmetic and make sure that you have marked the answer you in- tended to mark. The last two questions, which are each worth fifteen points, require written answers, and some partial credit might be given. However, no credit will be given for information that is not germane to the problem at hand. Please make sure to write your name and stu- dent ID number on the pages that include your answers to the last two questions. In fact, you will get one point on each of these two questions for writing your name and ID number legibly.

Use the Trapezoidal Rule with n = 4 to approximate the integral (^) ∫ 5 1

x dx (a) ln(5) (b) 5/ (c) 11/ (d) 19/ (e) 101/ (f) 103/ (g) 1. (h) 2.

How large do we have to choose n so that the error in using Simpson’s Rule to approximate ∫ (^17) 1

x^4 dx is less than 10−^4. (a) 1 (b) 2 (c) 16 (d) 24 (e) 134 (f) 472 (g) 26, (h) 46,

Compute (^) ∫ ∞ e

x(lnx)^3 dx (a) diverges to ∞ (b) diverges to −∞ (c) diverges but not to ∞ or −∞ (d) converges to e (e) converges to −e (f) converges to 1 (g) converges to e − 1 (h) converges to 1/ 2

Find the area of the region bounded by the curves x = 1 − y^2 and x = y^2 − 1. (a) 2 (b) 0 (c) 2 − 2 y^2 (d) 1 −

(e) 1 (f) 4/ 3 (g) 8/ 3 (h) 15/ 4

Compute the volume of the solid obtained by ro- tating the region in the first quadrant bounded by y = x^2 , y = 4 and x = 0 about the y-axis. (a) (^403)

2 π (b) 8π (c) 32π/ 5 (d) 16/ 3 (e) 16π/ 3 (f) 16π^2 / 3 (g) 64π/ 3 (h) 12π

Compute the volume of the solid obtained by rotat- ing about the line x = −1 the region bounded by y = sin x, y = 0, 0 ≤ x ≤ π/2. (a) 1 (b) π (c) 2π (d) 4π (e) (1 +

2)π (f)

3 π/ 2 (g)

3 π (h) 2

3 π

Find the exact length of the curve given parametri- cally by x = 1 + 3t^2 ; y = 4 + t^3 where 0 ≤ t ≤

(a) 1 (b) 19 (c) 25 (d) 45 (e) 3

(f) 5

(g) 6

(h) 9

Find the average value of f (x) = (^) xln x^1 on the interval [e, e^2 ]. (a) (^1) e (b) (^) e−^11 (c) (^) e+1^1 (d) (^) e (^21) −e (e) (^) e (^22) −e (f) (^) eln (^2) −^2 e (g) ln e( 2 ln−e2) (h) ( eln (^2) −2)e^2

Let f (x) = c/(1 + x^2 ). For what values of c is f a probability density function? (a) no value of c makes f a probability density func- tion (b) 0 (c) 1 (d) π/ 2 (e) −π/ 2 (f) 2/π (g) − 2 /π (h) π−^1

Name: Student ID:

Find the volume of the solid generated by revolving the region bounded by y = 1 − x^2 and the x-axis about the line x = −4. (a) Use Method I (disc/washer method) (b) Use Method II (cylindrical shells method)

Name: Student ID:

Evaluate (^) ∫ (^2)

0 ln x dx Show all work.

Name: Student ID:

Math 132, Spring 2011 - Exam 2: Integration and Approximation Questions, Exams of Calculus

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Download Math 132, Spring 2011 - Exam 2: Integration and Approximation Questions and more Exams Calculus in PDF only on Docsity!

NAME:

STUDENT ID NUMBER: