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### 75rev1-06

Course: MATH 75 - 76, Spring 2006
School: Lehigh
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Word Count: 391

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75 Math Fall 2006, Lehigh University, Exam I review These are a sampling of problems for review for the first 4o clock test. This sample may not be complete, and is not representative of the test questions. Be sure to prepare from all material from class and homeworks. Remember that use of calculators will not be allowed during the exam. Solve the inequality |2x - 3| &lt; 5 Solve the inequality 2x2 - 6x - 8...

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75 Math Fall 2006, Lehigh University, Exam I review These are a sampling of problems for review for the first 4o clock test. This sample may not be complete, and is not representative of the test questions. Be sure to prepare from all material from class and homeworks. Remember that use of calculators will not be allowed during the exam. Solve the inequality |2x - 3| < 5 Solve the inequality 2x2 - 6x - 8 > 0 Solve the inequality x2 - x + 1 0. Solve for x: |x + 3| = |2x + 1|. Sketch the region {(x, y)| - 2 - 2x y 4 - x} Solve for x assuming a, b, c are positive constants: a(b - cx) b/a (a) Find the equation of the line through (-4, 6) and parallel to the x-axis. (b) Find the equation of the line through (-4, 6) and parallel to the y-axis. 8. Find the equation of the line through (-3, 4) with slope 2. 9. Find the equation of the line through (4, 5) parallel to 2y = 4x + 5. 10. Identify and sketch the graph of the equation: x2 + y 2 - 6x + 2y = 6 11. Identify and sketch the graph of the equation: y = x2 + 1 12. (a) Convert 2/3 radians to degrees. (b) Find sin(2/3) and cos(2/3)? (you may use sin(/6) = 1/2 = cos(/3) and cos(/6) = 3/2 = sin(/3)) 13. If sin() = 4/5 for < 0 < /2 what are cos() and tan()? 14. Find the remaining trigonometric ratios. sec() = -1.5 and < < . 2 15. Find all values of x in the interval [0, 2] that satisfy sin(x) = tan(x). 16. Find all values of x in the interval [0, 2] that satisfy 2 sin2 (x) > 1. x-1 17. Find the domain of the following function: f (x) = x2 -1 18. Express the surface area of a cube as a function of its volume. 19. A rectangle has area 30 square meters. Express the perimeter of the rectangle as a function of the length of one of its sides. 20. The manager of a furniture factory finds that it costs \$2200 to manufacture 100 chairs one day and \$ 4800 to produce 300 chairs in another day. Assuming a linear relationship between the cost and the number of chairs produced, find the cost if the factory produced 200 chairs. 21. If f (x) = x2 - x + 2 find f (-2), f (a2 ), [f (a)]2 and f (x+h)-f (x) . Simplify the last h answer. 1. 2. 3. 4. 5. 6. 7. 22. Match each equation with its graph(graph1 or graph2 or graph3). Explain your choices. (a) y = x2 (b) y = x5 (c) y = x8 graph2 30 20 10 150 -2 0 -1 0 -10 x -20 -30 -2 -1 2 1 2 1 0 0 100 50 1 2 -2 -1 0 0 1 2 graph3 4 3 graph1 250 200
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Lehigh - MATH - 75 - 76
ASSIGNED PROBLEMS-MATH 75 APPENDIX A 1. Solve the inequality: 2 &lt; |3 - x| 82.Solve the equation: |2x - 3| = |3 - x| 3.Solve the inequality: x2 - 3x - 10 &gt; 0APPENDIX B 1. Find the equation for the line passing through (2,9) with a y-intercept of
Lehigh - MATH - 75 - 76
Calculus IThis document was written and copyrighted by Paul Dawkins. Use of this document and its online version is governed by the Terms and Conditions of Use located at http:/tutorial.math.lamar.edu/terms.asp. The online version of this document
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Algorithms in Systems Engineering IE170 Lecture 7Dr. Ted RalphsIE170 Lecture 71References for Today's Lecture Required reading CLRS Chapter 6 References D.E. Knuth, The Art of Computer Programming, Volume 3: Sorting and Searching (Third Ed
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Previous Lecture Maxwell's Equations Phasors for ac circuitsOctober 29, 2007 p.Today Exam and Schedule Issues More on Phasors Transformers (not on test) p.Hour Exam Info for 95% of youIf you have no conflicts and are not authorized
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Previous Lecture Model for Current Resistors in series and parallel Kirchhoff's Rules p.RC CircuitsAdd capacitors to the circuits. p.Nomenclature Steady-state Time-dependent (transient) p.RC CircuitsSwitch is closed at t = 0, and
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Previous Lecture Ucap = u=1 2 CV 2for capacitorEnergy is stored in electric field:2 1 0E 2 Dielectric constant K Current I is flow of charge p.Current: Realistic ModelSmall drift velocity vd superimposed on large random motion (vr
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IE 170 Final Examination Practice ProblemsDr. T.K. Ralphs1. (from David Eppstein, UC Irvine) Suppose you are implementing a spreadsheet program in which you must maintain a grid of cells. Some cells contain values, while other cells contain formul
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Previous LectureV and E are related: V (r) = - E = -VP rE dlCapacitors in series and parallel: Ceff = C1 + C2 parallel 1 1 1 = + series Ceff C1 C2 p.EnergyIt takes work to build up a charge on a capacitor. p.EnergyIt takes work to bui
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Previous Lecture Mutual inductance Self inductanceLR circuitsOctober 22, 2007 p.Hour Exam 2 Thursday, Nov. 1 at 4:10 pm LL270, Whitaker 303, &amp; Williams 301 Covers reading assignments through L-18 (end of Ch. 31) More on the web this we
Lehigh - IE - 426
IE426 Problem Set #1Prof Jeff LinderothIE 426 Problem Set #1Due Date: September 14, 2006. 4:30PM.1Convex FunctionsCategorize each of the functions below as convex, concave, or nonconvex over its domain. Note: Be sure to consider whether o
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Previous LectureWe completed the geometric optics of lenses and mirrors: location of images index of refraction dispersion total internal reflection Lensmaker's Equation one and two lens systems optical aberrations p.Geometric Optics L
Lehigh - PHYSICS - 21
Previous LectureMechanical waves satisfy the Wave Equation1 2D 2D - 2 2 =0 x2 v tNovember 12, 2007 p.Today Energy transport in waves Maxwell's Equations have wave-like solutions. p.Energy transportMechanical waves transport energy
Lehigh - ENGR - 1
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Lehigh - ENGR - 1
int i,j; /&lt;- BUBBLE SORT double temp1,temp2; for(i=0;i&lt;n;i+) /n is the number of memory locations needing to be sorted { for(j=0;j&lt;n-1;j+) { if(array[j]&gt;array[j+1]) { temp1=array[j]; temp2=array[j+1]; array[j]=temp2; array[j+1]=temp1; } } } / finds t
Lehigh - IE - 426
IE426 Problem Set #2 AnswersProf Jeff LinderothIE 426 Problem Set #2 - Answers1LP KnowledgeFor each of the problems in this section, you should determine which of the characterizations below best describes the linear program. The linear p
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IE426 Problem Set #1Prof Jeff LinderothIE 426 Problem Set #1 Answers 1 Convex FunctionsCategorize each of the functions below as convex, concave, or nonconvex over its domain. Note: Be sure to consider whether or not each function is in more t
Lehigh - IE - 426
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Lehigh - ME - 242
ME 242 Mechanical Engineering Systems Educational Outcomes-Fall 2005 Please circle the number that indicates how well you think you could perform each learning objective below after completing this course. Do this assuming that you would be working o
Lehigh - ME - 242
ME 242 Mechanical Engineering Systems N. D. Perreira, 8-29-2005 Learning Objectives. Upon completion of this course, students should be able to: 1. Assign an appropriate role to dynamic modeling and analysis in the design of complex mechanical engine
Lehigh - ME - 242
(Fall 2000) A system is modeled by the differential equationsdp = 3q - 6 dt dq = -3q - 3 p dt Determine the values and the names of whichever of the following parameters that apply: n , d , ,.First use operator notation to get, sp = 3q - 6 and
Lehigh - ME - 242
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Lehigh - ME - 242
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IE 426 Quiz #1 Answers11.1Short(ish) AnswerEasy or HardNote: In this subsection, I am NOT asking you to solve the problem. Rather, I am asking you to say whether, given the &quot;shape&quot; of the objective function (over the feasible region) and the &quot;
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Lehigh - IE - 426
IE426 Problem Set #4Prof Jeff LinderothIE 426 Problem Set #4Due Date: November 30, 2006. 4:30PM.1My Brown Eyed GirlMy long-haired friend Jim Sawyer is down on his luck. He has, however, concocted a new get-rich-quick scheme. Every morning
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Lehigh - ME - 242
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Lehigh - ME - 242
(Spring 2000) A linear model characterized by the transfer function S G(S ) = 2 . S + 2S + 2 with zero initial conditions, is excited by the following excitations. Determine the forced responses. a. u(t ) = 3 . Note that there are three ways to solve
Lehigh - IE - 426
IE 426 Quiz #2November 14, 2005 4:105:25READ THIS! Please put your name on all the pages of the exam. If you need more space, feel free to use the backs of the sheets, just make sure that I know where you are writing your answers. The more cle
Lehigh - IE - 426
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Lehigh - IE - 170
Algorithms in Systems Engineering IE170 Lecture 4Dr. Ted RalphsIE170 Lecture 41References for Today's Lecture Required reading CLRS Chapter 3 References R. Miller and L. Boxer, Algorithms: Sequential and Parallel, 2000. R. Sedgewick, Algo
Lehigh - IE - 170
Algorithms in Systems Engineering IE170 Lecture 5Dr. Ted RalphsIE170 Lecture 51References for Today's Lecture Required reading CLRS Chapter 2 References R. Sedgewick, Algorithms in C+ (Third Edition), 1998.IE170 Lecture 52Recursion
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Lehigh - PHYSICS - 21
Physics 21 Fall 2007Solution to HW-23Transformers Consider the transformer ideal unless otherwise noted. (A) The primary coil of a transformer contains 100 turns; the secondary has 200 turns. The primary coil is connected to a size AA battery tha
Lehigh - MATH - 23
Math 23, Spring 2005 B. Dodson J. Mohler1. Course Info 2. Week 1 Homework: 12.1, 12.2 Distance, vectorsProblem 12.1.15: Show that the equation x2 + y 2 + z 2 - 6x + 4y - 2z = 11 represents a sphere, and find its center and radius. Solution: (x -
Lehigh - MATH - 23
Math 23 Sections 110-113 B. Dodson Week 2 Homework: 12.2 vectors: unit, standard unit, notations 12.3 dot product: orthogonal, proj, comp 12.4 cross product: formula, propertiesProblem 12.2.25: Find a unit vector u that has the same direction as a
Lehigh - MATH - 23
Math 23 Sections 110-113 B. Dodson Week 3 Homework: 12.5 Lines, Planes 12.6 Quadratic Surfaces 12.7 Cylindrical and Spherical CoordsProblem 12.5.3: Give vector and (scalar) parametric equations for the line through the point (-2,4,10) parallel to t
Lehigh - MATH - 23
Math 23 Sections 110-113 B. Dodson Week 4 Homework: 13.1, 13.2 vector functions, derivatives 13.3 arc length, curvature 13.4 velocity, accelerationProblem 13.2.9: Find the derivative of the vector function r(t) =&lt; t2 , 1 - t, t &gt;. Solution: We jus
Lehigh - MATH - 23
Math 23 Sections 110-113 B. Dodson Week 5 Homework: 14.1 graphs, level curves/surfaces, contour maps 14.2 limitsProblem 14.1.9b: 2 2 Find the domain of f (x, y, z) = e z-x -y .Solution: By definition, the domain of a function defined by a formu
Lehigh - PHYSICS - 21
29-45 In the circuit shown, the capacitor has capacitance C=20 F and is initially charged to 100 V with the polarity shown. The resistor R_0 has resistance 10 . At time t=0 the switch is closed. The small circuit is not connected in any way to the la
Lehigh - MATH - 23
Math 23, Spring 2007 B. Dodson X. Li1. Course Info 2. Week 1 Homework: 12.1: 3-Space, Distance Note: weekly slides (these) will be posted on blackboard.daily slides (larger font, more pages) may be found on http:/www.lehigh.edu/ bad0/coursesPro
Lehigh - MATH - 23
Math 23 B. Dodson Week 2 Homework: 12.2 vectors: unit, standard unit, notations 12.3 dot product: orthogonal, proj, comp 12.4 cross product: formula, properties Problem 12.2.19a: Find |a| and a - 2b when a =&lt; 6, 2, 3 &gt;, b =&lt; -1, 5, -2 &gt; . Solution: T
Lehigh - MAT - 141
1FormulasRemember, mathematics is all about being lazy. Using the limit definition of the derivative will get very difficult if we have to do it every time. Fortunately, we have methods for computing common derivatives like we have methods for co
Lehigh - MAT - 141
11.1ContinuityDefinitionsLast time, I went over the direct substitution property. That says that for polynomials and rational functions, as long as a is in the domain, lim f (x) = f (a). It turns out that this property works for a lot of differ
Lehigh - MAT - 141
1Tangents and velocitiesOn the first day, I talked very briefly about where calculus comes from. One branch comes from studying tangent lines to curves. Here's a more in-depth overview. A tangent line to a circle is basic. (draw picture) But a ta
Lehigh - MAT - 141
11.1TrigonometryAnglesI mentioned on Tuesday that we don't use degrees in calculus. Instead we use a unit called radians. Definition 1. One radian is the angle that gives an arc length equal to the radius. Since the circumference of a circle is
Lehigh - MAT - 141
11.1FunctionsWhat is a function?All a function is, is something that takes a number and turns it into another number. Example 1.1. Remember from geometry class the formula for a circle, A = r2 . This is a nice example of a function. It takes a
Lehigh - MAT - 141
Homework # 2 Due: 5/30/06 1. Use the graph to find the following limits: lim f (x) lim f (x) lim f (x) lim f (x) lim f (x)x2+ x0x2-x2x-12. Sketch the graph of a function that satisfies all of the given conditions: lim f (x) = 1 lim f (x) =
Lehigh - MAT - 141
Homework # 4 Due: 6/13/06 1. Differentiate the following: (a) f (x) = x2 (cos x)(sin x) (b) f (x) = (c) f () = (d) f (x) =tan x-1 sec x sin (+tan ) 1+sec (x-1)4 (x2 +2x)5(e) f (x) = sin tansin x2. Find dy/dx by implicit differentiation: (a)
Lehigh - MAT - 141
Homework # 1 Due: 05/23/06 #1 Find the domain of the following functions 3x2 - 2x + 1 a) f (x) = 2 x - 4x - 21 3 b) f (x) = x + 3 - x - 2 + x2 - 1 1 c) f (x) = x2 - 1 #2 Graph the following piecewise function f (x) = #3 1.2 # 2 #4 1.2 # 12 #5 f
Lehigh - MAT - 141
Quiz # 1 Name: 1. Find f (2 + h), f (x + h), and f (x + h) - f (x) if f (x) = x - x2 . h2. Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, or transcendental function (
Lehigh - MAT - 141
Homework # 3 Due: 6/6/06 1. Find an equation of the tangent line to y = 2x + 1 at the point (4,3).The equation of a tangent line to y = f (x) at (a, b) is (y - b) = f (a)(x - a). First, we 1 write the equation as y = (2x + 1) 21 d (2x + 1) 2 dx
Lehigh - MAT - 141
1Tangents and VelocitiesRecall finding tangents numerically.1.1TangentsRemember formula for slope of secant line. Definition 1. The tangent line to the curve y = f (x) at the point (a, f (a) is the line through the point with slope f (x) -
Lehigh - MATH - 23
Week 14 Homework:[due Mon, Wed, and Fri]16.7 Surface integrals (on graphs, lecture note) [due Mon] 16.8 Stokes' Theorem [due Wed] 16.9 Divergence Theorem [due Fri]Problem 16.9.7: Use the Divergence Theorem to calculate the surface integralSF
Lehigh - MATH - 23
Math 23 B. Dodson Week 12 Homework: [due April 13]16.1, 16.2 vector fields and line integrals Week 13 Homework: [due April 20]16.3 Fundamental Theorem for line integrals 16.4 Green's Formula 16.5 Curl and Divergence [Slides for Week 11 Homework a
Lehigh - MATH - 23
Math 23 B. Dodson Week 10 Homework: 15.5 Applications (mass, center of mass) 15.6 Surface AreaProblem 15.5.6: Find the mass and center of mass of a thin plate (lamina) occupying the triangular region with verticies at (0, 0), (1, 1) and (4, 0), if
Lehigh - MATH - 23
Math 23 B. Dodson Week 3 Homework: 12.5 Lines, Planes 12.6 Quadratic Surfaces 12.7 Cylindrical and Spherical CoordsProblem 12.5.3: Give vector and (scalar) parametric equations for the line through the point (-2,4,10) parallel to the vector &lt; 3, 1,
Lehigh - MATH - 23
Math 23 B. Dodson Week 5: 13.3 arc length, curvature 13.4 velocity, acceleration; 14.1 functions of several variablesWeek 5 Homework: 13.3 curvature (Mon) Problem 13.3.16 Use formula (9) to find the curvature of r(t) =&lt; t2 , 2t, ln t &gt;. Solution: W