Math 16B, Section 1 Sarason MIDTERM EXAMINATION 2 SOLUTIONS 1. Perform the integrations.
Spring 2006
(a) I1 =
0
x sin(x2 )dx
(b) I2 =
0
x2 sin x dx
Solution. (a) We make the substitution u = x2 , du = 2x dx: I1 1 = 2 1 sin u du = cos u 2 0 1 1 = (1) + (
Midterm2 Review
This review is not comprehensive and students are encouraged to review additional material from lecture and discussion. Energy Metabolism 1. Which are the energy sources that can be converted to glucose? 2. What can the glucose in the bloo
Math 16B S06 Supplementary Notes 6 Error Estimate for Approximation by Taylor Polynomials Recall that the nth Taylor polynomial for the function f (x) at the point x = a is the polynomial f (a) + f (a)(x a) + f (a) f (3) (a) f (n) (a) (x a)2 + (x a)3 + +
Math 16B S06 Supplementary Notes 5 The Dierential Notation The dierential notation is a convenient formalism which, once one becomes accustomed to it, can often provide a smooth way of carrying out integrations. The dierential df (x) of the function f (x)
Math 16B S06 Supplementary Notes 4 The Derivatives of sin t and cos t One can derive the formulas (1) starting from the relations (2) lim sin t =1 t0 t cos t 1 = 0. t d (sin t) = cos t, dt d (cos t) = sin t dt
(3)
lim
t0
Note that (2) and (3) just say tha
Math 16B S06 Supplementary Notes 3 The Lagrange Multiplier Method The method of Lagrange multipliers is often eective in nding solutions of constrained extremum problems. In the two-variable version of such a problem, one is given a function f (x, y ), an
Math 16B S06 Supplementary Notes 2 Second-Derivative Test To understand what is behind the second-derivative test for functions of two variables, we shall start by looking at the simplest nontrivial example, that of a polynomial of degree 2. First the tes
Math 16B S06 Supplementary Notes 1 The Derivative and Local Linear Approximation For a function g (x) of one variable, the value g (a) of the derivative of g at the point x = a is the slope of the tangent line to the graph of g at the point (a, g (a). Nea
Math 16B, Section 1 Sarason REVIEW EXERCISES 3
Spring 2006
1. In each part, nd and classify (by means of the second-derivative test) the critical points of the function f . (a) f (x, y ) = 8x3 + y 3 xy (b) f (x, y ) = 5x2 + y 2 x y 2xy 2. Which pair of va
Math 16B, Section 1 Sarason REVIEW EXERCISES 2
Spring 2006
1. A surveyor measures the angle of elevation of the top of a building as seen from a spot on the ground 100 feet from the building and nds it to be 1.25 radians. Estimate the height of the buildi
Math 16B, Section 1 Sarason REVIEW EXERCISES 1 1. In each part, nd all rst and second partial derivatives of the given function. 2 2 2 (a) f (x, y ) = (x2 + y 2 )3/2 (b) f (x, y ) = e(x +y z ) (c) f (x, y ) = ln(x2 + y 2 )
Spring 2006
2. (Midterm, F05) In
Type of Free Fatty Acid (FFA) Name of FFA Saturated fatty acid- Short, Butyrate (short chain) medium and long chain Myristate (medium chain) Palmitic acid or Palmitate (long chain) Stearic acid or Stearate (long chain) Monounsaturated fatty acid Palmitole
Lect 13 Fat Soluble Vitamins Study Questions (Also for Lecture 14) Describe how the digestion of fat soluble vitamins is different that the digestion of a water soluble nutrient. What are the functions of Vitamin A? What is the difference between b-carote
Lect 12 Iron and Immunity Study Questions Describe the differences in structure and function between hemoglobin and myoglobin. What are the effects of too little iron? Too much iron? What is the difference between heme iron and non-heme iron? What foods c
LECT 11 Study Questions: Water What is the difference between intracellular and extracellular water? Give examples of each. What are the functions of electrolytes? Name foods high in sodium and potassium. What happens if we dont consume sufficient water?
What are the symptoms of alcohol poisoning? What are the treatments for alcohol poisoning? Describe the reactions catalyzed by the 3 enzymes involved in alcohol metabolism. What factors affect alcohol dehydrogenase activity? What are the metabolic consequ
Lect 9 Metabolism Study Questions
Fall 2009
1. What types of enzyme reactions require ATP? What types give off ATP? 2. Why cant fatty acids provide glucose for energy for the brain? What other types of energy sources can be converted into glucose? 3. What
New Student Services Education 98, Sections 27, 28 and 29: CALeads Leadership Philosophy Paper Assignment A key goal of this class is to help you articulate your philosophy on leadership. For this assignment, you will attempt to think about the deeper mea
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ANTHRO 2AC: INTRODUCTION TO ARCHAEOLOGY FALL SEMESTER 2010 MWF 11-12; 4 units; 2050 Valley Life Science Building INSTRUCTOR: Kent Lightfoot, Professor of Anthropology Office: 2251 College Building, Room 213; Phone: 510-642-1309; klightfoot@berkeley.edu
Be neand Arom nze aticity
1825 Faraday discove be neby pyrolysis of whaleoil: C rs nze olorle ss liquid bp ~80C Ve unre . ry unre active . Analysis: C: H 1 :1
Michae Faraday l Michae 1791-1867 1791-1867
S ynthe Mitsche sis: rlich by che ical m de gradatio
Peter Vollhardt University of California at Berkeley
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TigreDe Bue Aire 1952 lta, nos s,
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Chapter 14 Delocalized Pi Systems Delocalized
Re thedoublebond call
Trigonal The bond is e rich: -rich: The E attack, attack add) add
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Peter Vollhardt University of California at Berkeley
I, too, star
Ti gr e Del ta, Buenos Ai r es, 1952
te d
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Chapter 14 Delocalized Pi Systems Delocalized
Recal l the doubl e bond Recal
Tr i gonal T he bond i s eThe r i ch: E attack , attack R add )
Peter Vollhardt University of California at Berkeley
I, too, star
TigreDe Bue Aire 1952 lta, nos s,
te d
small.
Chapter 14 Delocalized Pi Systems Delocalized
Re thedoublebond call
Trigonal The bond is e rich: -rich: The E attack, attack add) add
Thelobe o
X-Men: Icon of an Evolving Political Culture (Fall 2009)
X-Men, created in 1963 by Stan Lee & Jack Kirby, is the most popular comic series in the Marvel Universe. The X-Men are fictitious mutants who, as a result of a sudden leap in evolution, are born wi