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Michigan State University | MATH 133
Professors
- Wei,
- Hensh,
- Kurtz,
- Thomas H Parker,
- Kulkarni,
- Lamm,
- Mao Dong,
- Abbas
Relevant Courses
100 sample documents related to MATH 133
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Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number 11.3 is due : 04/05/2010 at 06:00am EDT. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with your questions. The primary purpose of -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number 11.4 is due : 04/05/2010 at 06:00am EDT. IMPORTANT: Look for orange-colored text written above the online list of homework problems for this set to tell you whether the due date for 1 -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number 11.5 is due : 04/05/2010 at 06:00am EDT. IMPORTANT: Look for orange-colored text written above the online list of homework problems for this set to tell you whether the due date for 1 -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number 8.5 is due : 03/08/2010 at 06:00am EST. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with your questions. The primary purpose of W -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number 8.8 is due : 03/08/2010 at 06:00am EST. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with your questions. The primary purpose of W -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number 9.1 is due : 03/22/2010 at 06:00am EDT. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with your questions. The primary purpose of W -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number 11.1 is due : 03/22/2010 at 06:00am EDT. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with your questions. The primary purpose of -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number OPTIONAL-Exam2-ReviewProblems 7.7 to 8.4 is due : 02/24/2010 at 11:59pm EST. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with you -
Michigan State University MATH 133
Nicholas Charles Miller MTH 133 KURTZ 133.007 WeBWorK assignment number OPTIONAL-Exam1-ReviewProblems 6.1 to 7.6 is due : 02/03/2010 at 11:59pm EST. For help on any of these problems, please consult the MTH 133 WeBWorK Forum or start a new thread with you -
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Michigan State University MATH 133
Quiz 8 Name_ Section_ TA_ Test for convergence or divergence. 1. ln n n2 ln(n + 1) n=2 1 n2 < n=2 Compare to n n=2 1 2 using the direct comparison ln n 1 2, n ln(n + 1) n 2 thus n n=2 2 ln n <. ln(n + 1) Alternatively, we could use the limit comparison te -
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Michigan State University MATH 133
1. a. dy 1 3 = 3 = 2 1 + 9x 1 + 9x 2 dx 2 6x (ln (x 2 + 1) 2 1 dy 2 = 3 (ln (x + 1) 2 2x = b. dx x +1 x2 + 1 c. ln y = sin1 x ln x 1 dy 1 1 = ln x + sin1 x 2 y dx x 1x ln x 1 sin1 x dy = x sin x + 1 x2 dx x 1 dy = x (y 1) dy = y 1 dx 2. x2 x dx ln y 1 = x -
Michigan State University MATH 133
Quiz 4 Name_ Section_ TA_ 1. Compute dy if y = sin -1 ( 1 - x 2 ) . Simplify your answer. dx 1 dy 1 -1 (1 - x 2 ) 2 (-2 x) = dx 1 - (1 - x 2 ) 2 2. Compute 8 + 2x 0 2 dx 2 . 8 + 2x 0 2 dx 2 = 1 dx 1 dx x 2 = 8 x 2 80 0 1+ -
Michigan State University MATH 133
Quiz 5 Solution 1. Compute dy if y = ln(tanh 2 x) . dx dy 1 2 = sech 2 x 2 dx tanh 2 x ( ) 2. Compute x 0 1 2 cosh(2 x)dx . Diff x2 2x Int cosh 2x 1 sinh 2 x 2 2 1 cosh 2 x 4 1 sinh 2 x 8 1 2 0 1 x2 x 1 x cosh(2 x)dx = sinh -
Michigan State University MATH 133
Math 133 Dr. Kurtz Exam 1 Name_ Section No._ TA_ Instructions: Please show all of your work. Credit will not be given for answers with no supporting work. dy 1. (21 pts) Compute . dx 2 e- x y= 2 (a) x 2 2 x 2 e - x (-2 x) - e- x (2 x) = Quotient r -
Michigan State University MATH 133
Math 133 Dr. Kurtz Exam 2 Name_ Section No._ TA_ Instructions: Please show all of your work. Credit will not be given for answers with no supporting work. 1. (18 pts) For each rational function, determine the correct form of the partial fractions -
Michigan State University MATH 133
Exam 3 solutions Instructions: Please show all of your work. Credit will not be given for answers with no supporting work. 1.(20 pts) Compute each of the improper integrals. (a) t dx 1 2dx 1 1 1 -1 -1 -1 (1 + 4 x 2 ) = lim 2 1 + (2 x)2 = lim -
Michigan State University MATH 133
Math 133 Exam 4 Name_ Section_ TA_ Instructions: Please show your work. An answer alone with no supporting work will receive no credit. __ 1.(45 pts) Classify each of the following series as either convergent or divergent. Name the test you are us -
Michigan State University MATH 133
Quiz 6 Solution 1. Evaluate tan 0 4 3 x dx tan 0 4 3 x dx = 0 4 1 1 1 1 4 1 tan x sec x - 1 dx = tan 2 x + ln cos x = + ln = - ln 2 2 2 0 2 2 2 ( 2 ) 2. Evaluate 2 2 4 dx x2 - 4 x = 2sec = sec -1 x 2 Su -
Michigan State University MATH 133
Quiz 7 Solution 1. Solve each differential equation. Write your solution y explicitly as a function of x. (a) dy 1 + y 2 = dx x ; y (1) = 1 Separation of variables leads to dy dx = 2 x 1+ y dy dx 1+ y2 = x tan -1 y = ln x + C Requiring y (1) = -
Michigan State University MATH 133
Quiz 8 solution Test for convergence or divergence. Please be clear about what test you are using and how you are using it. 1. ln n n2 n=2 Compare to n=2 1 n 3 2 . ln n 1 2 ln n 2 lim n = lim 1 = lim n 1 = lim 1 = 0 n 1 n n 1 - n n2 -
Michigan State University MATH 133
Quiz 9 Name_ Section_ TA_ Determine the radius of convergence as well as the precise interval of convergence for the power xn series . In other words, you should check the endpoints of the interval as well. 2 n n = 0 ( n + 1) 3 Please show all wo -
Michigan State University MATH 133
Quiz 10 Name_ Section_ TA_ 1. Find the Maclaurin series for f ( x) = x 2 e - x 2 x - k k +2 2 = (-1) x 2 f ( x) = x 2k k ! k! k =0 k =0 k 2. Find the Taylor polynomial P3 ( x) for f ( x) = tan x (a = 0) . f ( x) = tan x f ( x) = se -
Michigan State University MATH 133
8.5 1 8.5 2 8.5 Trigonometric Substitution Three Basic Substitutions Recall the derivative formulas for the inverse trigonometric functions of sine, secant, tangent. (1) (2) (3) d 1 sin-1 x = , |x| < 1 dx 1 - x2 1 d tan-1 x = dx 1 + x2 d 1 , |x -
Michigan State University MATH 133
8.4 1 8.4 2 8.4 Trigonometric Integrals Products of Powers of Sines and Cosines These formulas are very useful when integrating even powers of sine and cosine. Example 1. Evaluate the following integrals. a. cos2 x dx By (1) we have cos2 x dx = -
Michigan State University MATH 133
8.8 1 8.8 2 8.8 Improper Integrals Type I - Infinite Limits of Integration Now, what happens in (2) as b ? In this case we have the following. 1 Consider the following example. Example 1. Infinite Areas? Suppose that b > 1. Evaluate the follo -
Michigan State University MATH 133
Quiz 1 Name_ Section_ TA_ The finite region bounded by y = x 2 and y = 4 is rotated about the x-axis. Find the volume of the solid formed. You should include a reasonable sketch of the solid. Please set up the integral completely, but you do not need -
Michigan State University MATH 133
Quiz 2 Name_ Section_ TA_ Set up completely an integral for the work done in emptying a full conical water reservoir of height 15 feet and radius 15 feet at the top by pumping the water to a height of 5 feet above the top of the reservoir. Water we -
Michigan State University MATH 133
Quiz 3 Name_ Section_ TA_ 1. Compute dy if y = (cos x) ln(sin x) . dx dy cos x = (- sin) ln(sin x) + cos x dx sin x 2. Compute the antiderivative. e3 x (1 + e3 x )3 dx Substitute u = 1 + e3 x , du = 3e3 x dx , which leads to e3 x 1 du -
Michigan State University MATH 133
Quiz 4 Name_ Section_ TA_ 1. Compute dy if y = sin -1 ( 1 - x 2 ) . Simplify your answer. dx 1 dy 1 -1 (1 - x 2 ) 2 (-2 x) = dx 1 - (1 - x 2 ) 2 2. Compute 8 + 2x 0 2 dx 2 . 8 + 2x 0 2 dx 2 = 1 dx 1 dx x 2 = 8 x 2 80 0 1+ -
Michigan State University MATH 133
Quiz 5 Solution 1. Compute dy if y = ln(tanh 2 x) . dx dy 1 2 = sech 2 x 2 dx tanh 2 x ( ) 2. Compute x 0 1 2 cosh(2 x)dx . Diff x2 2x Int cosh 2x 1 sinh 2 x 2 2 1 cosh 2 x 4 1 sinh 2 x 8 1 2 0 1 x2 x 1 x cosh(2 x)dx = sinh -
Michigan State University MATH 133
Formulas for Calculus II (MTH 133) Volume of a Solid: V = A(x) dx Length of Parametric Curves: L = ([f\'(t)]2 + [g\'(t)]2) dt Length of y = f(x): L = (1 + [f\'(x)]2) dx Length of x = g(y): L = (1 + [g\'(x)]2) dy Work: F(x) dx Hooke\'s Law: F = kx axb -
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Michigan State University MATH 133
Mathematics 133 Announcements April 11 Gateway Exam 2 ENDS TODAY. Quiz 9 Solutions are posted on the class webpage. Revised Scoring for Quiz/Gateway portion of your course grade: Quizzes and Gateway Exams contribute toward 100 out of the total of -
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Michigan State University MATH 133
Practice Problems for Math 133 Exam 4 Exam 4 will cover the material done in class and in homework from Sections 11.2 11.10 plus Sections 10.4 and 10.5. The problems on this sheet should help to remind you of this material. You should also go throug -
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Michigan State University MATH 133
Practice Problems for Math 133 Exam 3 1. Work out the following integrals using partial fractions. (a) 4x2 + 6 dx = ln x2 (x2 + 3) + C x3 + 3x x2 + x dx = ln(x - 1) + arctan x + C (x - 1)(x2 + 1) 1 x2 + 4 x x2 + x - 10 dx = ln + arctan + C (2x - 3)( -
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Michigan State University MATH 133
Math 133 Final Exam, Spring 2006 Name: _ PID: _ Total: _ Instructor: _ Section: _ Instructions: There are 10 pages, with a total of 200 possible points. You must show all necessary work to receive credit. Calculators are not allowed on this exam. -
Michigan State University MATH 133
Series Tests - Complete Summary Standard Series 1. Geometric Series n=0 Arn = A + Ar + Ar2 + = if |r| < 1 diverges if |r| 1 converges, 1 n A 1-r 2. p-Series 1 converges if and only if p > 1 (e.g. np 1 n2 diverges). 3. Constant Serie -
Michigan State University MATH 133
Math 133 Calculus 2 Sections 1 - 4, Spring 2008 Professor: Thomas H Parker A-346 Wells Hall 353-8493 parker@math.msu.edu Office hours: Monday 3: Katrin Ayrapetov A-1 -
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