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math150A_hw7

Course: MATH 715473, Fall 2009
School: CSU Northridge
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150A Calculus MATH I Fall 2007 Homework 7 Due: Tue. Oct. 23, 2007 For each of the functions below: I. nd its domain and range II. nd its x- and y-axis intercepts III. determine whether the graph is symmetric with respect to the y-axis or the origin IV. nd its asymptotes asymptotes (horizontal, vertical, and oblique) nd V. critical points, relative extrema and intervals where the function is...

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150A Calculus MATH I Fall 2007 Homework 7 Due: Tue. Oct. 23, 2007 For each of the functions below: I. nd its domain and range II. nd its x- and y-axis intercepts III. determine whether the graph is symmetric with respect to the y-axis or the origin IV. nd its asymptotes asymptotes (horizontal, vertical, and oblique) nd V. critical points, relative extrema and intervals where the function is increasing/decreasing VI. nd inection points and intervals where the function is concave up/down VII. s...

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CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 4 Due: Tue. Sept. 25, 2007 Section 3.3, pg. 145: 19, 25, 31, 37, 49, 59, 63, 95. Section 3.4, pg. 154: 1 15 (odd), 23, 33, 35, 37, 39, 45, 47. Section 3.5, pg. 161: 1, 5, 13, 21, 41, 53.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 4 Due: Tue. Sept. 25, 2007 Section 3.3, pg. 145: 19, 25, 31, 37, 49, 59, 63, 95. Section 3.4, pg. 154: 1 15 (odd), 23, 33, 35, 37, 39, 45, 47. Section 3.5, pg. 161: 1, 5, 13, 21, 41, 53.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 6 Due: Tue. Oct. 16, 2007 Section 3.9, pg. 193: 1, 3, 11, 17, 21, 31, 33, 35, 37. Section 4.1, pg. 211: 3, 5, 11, 17, 21, 25, 31, 35, 47, 53, 69. Section 4.2, pg. 219: 1, 5, 11, 19, 29, 33.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 6 Due: Tue. Oct. 16, 2007 Section 3.9, pg. 193: 1, 3, 11, 17, 21, 31, 33, 35, 37. Section 4.1, pg. 211: 3, 5, 11, 17, 21, 25, 31, 35, 47, 53, 69. Section 4.2, pg. 219: 1, 5, 11, 19, 29, 33.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 3 Due: Tue. Sept. 18, 2007 Section 3.1, pg. 119: 1, 3, 5, 7, 11, 17, 27, 43. Section 3.2, pg. 131: 3, 5, 7, 17, 23, 39, 51. Section 3.3, pg. 145: 1 11 every odd.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 3 Due: Tue. Sept. 18, 2007 Section 3.1, pg. 119: 1, 3, 5, 7, 11, 17, 27, 43. Section 3.2, pg. 131: 3, 5, 7, 17, 23, 39, 51. Section 3.3, pg. 145: 1 11 every odd.
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 6 Due: Thurs. Mar. 13, 2008 Section 12.4, pg. 640: 1, 3, 7, 11, 15, 17, 19, 21. Section 12.5, pg. 646: 5, 7, 9, 11, 13, 19, 21, 25. Section 12.6, pg. 651: 1, 3, 5, 9, 13, 19, 21, 31.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 6 Due: Thurs. Mar. 13, 2008 Section 12.4, pg. 640: 1, 3, 7, 11, 15, 17, 19, 21. Section 12.5, pg. 646: 5, 7, 9, 11, 13, 19, 21, 25. Section 12.6, pg. 651: 1, 3, 5, 9, 13, 19, 21, 31.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 9 Due: Thurs. Nov. 15, 2007 Section 5.1, pg. 299: 3, 17, 20, 21. Section 5.2, pg. 310: 3, 11, 17, 21, 29, 35, 53. Section 5.3, pg. 321: 5, 7, 19 25 (odds), 35. Additional Problems: 1. Prove:n n n(ai + bi
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 9 Due: Thurs. Nov. 15, 2007 Section 5.1, pg. 299: 3, 17, 20, 21. Section 5.2, pg. 310: 3, 11, 17, 21, 29, 35, 53. Section 5.3, pg. 321: 5, 7, 19 25 (odds), 35. Additional Problems: 1. Prove:n n n(ai + bi
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 5 Due: Thurs. Mar. 6, 2008 Section 12.1, pg. 622: 5, 21, 23, 25, 27, 33. Section 12.2, pg. 628: 1, 3, 5, 9, 27, 29, 33, 41. Section 12.3, pg. 634: 3, 15, 17, 19, 25, 27, 35.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 5 Due: Thurs. Mar. 6, 2008 Section 12.1, pg. 622: 5, 21, 23, 25, 27, 33. Section 12.2, pg. 628: 1, 3, 5, 9, 27, 29, 33, 41. Section 12.3, pg. 634: 3, 15, 17, 19, 25, 27, 35.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 2 Due: Tue. Sept. 11, 2007 Section 2.3, pg. 84: 47, 55. Section 2.4, pg. 95: 1, 11, 13, 15, 17 read section before attempting problems! Section 2.5, pg. 105: 1, 5, 7, 9, 13, 37, 41, 61, 62.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 2 Due: Tue. Sept. 11, 2007 Section 2.3, pg. 84: 47, 55. Section 2.4, pg. 95: 1, 11, 13, 15, 17 read section before attempting problems! Section 2.5, pg. 105: 1, 5, 7, 9, 13, 37, 41, 61, 62.
CSU Northridge - MATH - 581
MATH 581Numerical Methods for Linear SystemsSpring 2008Homework 1 Due: Thurs. Feb. 7, 2008 Lecture Lecture Lecture Lecture 1, 2, 3, 4, pg. pg. pg. pg. 9: 1.1, 1.3 16: 2.1, 2.5, 2.6 24: 3.2, 3.3, 3.5 31: 4.1, 4.3Additional Problem 1. Let A be
CSU Northridge - MATH - 715473
MATH 581Numerical Methods for Linear SystemsSpring 2008Homework 1 Due: Thurs. Feb. 7, 2008 Lecture Lecture Lecture Lecture 1, 2, 3, 4, pg. pg. pg. pg. 9: 1.1, 1.3 16: 2.1, 2.5, 2.6 24: 3.2, 3.3, 3.5 31: 4.1, 4.3Additional Problem 1. Let A be
CSU Northridge - MATH - 53971
Math 550. Homework 8. Due 11/10/03Problem 1. Let U, V be open subsets of R2 . Prove that the coboundary map : H 0 (U V ) H 1 (U V ) is a homomorphism of vector spaces. Problem 2. Let F : U V be a smooth map from the open set U R2 into the open
CSU Northridge - MATH - 550
Math 550. Homework 8. Due 11/10/03Problem 1. Let U, V be open subsets of R2 . Prove that the coboundary map : H 0 (U V ) H 1 (U V ) is a homomorphism of vector spaces. Problem 2. Let F : U V be a smooth map from the open set U R2 into the open
CSU Northridge - MATH - 311
Math 311. Quiz 5 Due: Monday, October 20, 2008Name:Construction a Golden Triangle We have proved that an isosceles triangle with long side equal to 1 and short of 51 side equal to is a golden triangle. Problem 1 uses this information in order to
CSU Northridge - MATH - 53971
Math 311. Quiz 5 Due: Monday, October 20, 2008Name:Construction a Golden Triangle We have proved that an isosceles triangle with long side equal to 1 and short of 51 side equal to is a golden triangle. Problem 1 uses this information in order to
CSU Northridge - MATH - 53971
Math 550. Homework 9. Due 12/03/03Problem 1. Suppose that U = R2 \ {P1 , , Pn } is the complement of n points in the plane. Prove that the mapping that takes a closed 1-chain to W (, P1 ), , W (, Pn ) determines an isomorphism of H1 U with t
CSU Northridge - MATH - 550
Math 550. Homework 9. Due 12/03/03Problem 1. Suppose that U = R2 \ {P1 , , Pn } is the complement of n points in the plane. Prove that the mapping that takes a closed 1-chain to W (, P1 ), , W (, Pn ) determines an isomorphism of H1 U with t
CSU Northridge - MATH - 53971
Math 550. Homework 7. Due 10/29/03Problem 1. A vector X in Rn is called a probability vector if its coordinates are all nonnegative and add up to 1. An n n matrix is an stochastic matrix if its columns are probability vectors. Use the Brouwer xed
CSU Northridge - MATH - 550
Math 550. Homework 7. Due 10/29/03Problem 1. A vector X in Rn is called a probability vector if its coordinates are all nonnegative and add up to 1. An n n matrix is an stochastic matrix if its columns are probability vectors. Use the Brouwer xed
CSU Northridge - MATH - 53971
Math 623. Homework 5. Due 04/21/04Problem 1. Show that the hyperbolic distance d(z, w) between points z and w in the unit disk satises the following identity 1 zw Tanh d(z, w) = . 2 1 zw Problem 2. A circle in H2 centered at p with radius r is the
CSU Northridge - MATH - 623
Math 623. Homework 5. Due 04/21/04Problem 1. Show that the hyperbolic distance d(z, w) between points z and w in the unit disk satises the following identity 1 zw Tanh d(z, w) = . 2 1 zw Problem 2. A circle in H2 centered at p with radius r is the
CSU Northridge - MATH - 53971
Math 655. Homework 3. Due 2/26/03Problem 1 Let f be an analytic function on a connected open set U C. (1) Show that if f is real valued, then f is constant on U . (2) Show that if f has constant absolute value, then f is constant on U . Problem 2
CSU Northridge - MATH - 655
Math 655. Homework 3. Due 2/26/03Problem 1 Let f be an analytic function on a connected open set U C. (1) Show that if f is real valued, then f is constant on U . (2) Show that if f has constant absolute value, then f is constant on U . Problem 2
CSU Northridge - MATH - 53971
Math 655. Homework 1. Due 2/5/03Problem 1 Prove thatab <1 1 abif |a| < 1 and |b| < 1. Prove also thatab =1 1 abif either |a| = 1 or |b| = 1. What exception must be made if |a| = |b| = 1? Problem 2 Show that the functions f (z) and f (z) a
CSU Northridge - MATH - 655
Math 655. Homework 1. Due 2/5/03Problem 1 Prove thatab <1 1 abif |a| < 1 and |b| < 1. Prove also thatab =1 1 abif either |a| = 1 or |b| = 1. What exception must be made if |a| = |b| = 1? Problem 2 Show that the functions f (z) and f (z) a
CSU Northridge - MATH - 53971
Math 592D. Homework 4. Due: 4/28/051. Problem 5.3.2 2. Problem 5.4.2
CSU Northridge - MATH - 592
Math 592D. Homework 4. Due: 4/28/051. Problem 5.3.2 2. Problem 5.4.2
CSU Northridge - MATH - 53971
Math 592D. Homework 3. Due: 3/10/05Do at least 2, 3, 4 (not 4(e). Then 1 if possible. 5 and 6 are suggestions. 1. The approach to modeling age-structured populations in continuous time is similar to what we have done in discrete time. If u(a, t) is
CSU Northridge - MATH - 592
Math 592D. Homework 3. Due: 3/10/05Do at least 2, 3, 4 (not 4(e). Then 1 if possible. 5 and 6 are suggestions. 1. The approach to modeling age-structured populations in continuous time is similar to what we have done in discrete time. If u(a, t) is
CSU Northridge - MATH - 53971
Math 550. Homework 2 (Revised). Due 9/22/2003Problem 1 Let U be the union of two open sets U1 ,U2 , i.e., U = U1 U2 . Let f j be a smooth functions on U j , j = 1, 2, such that f1 (x) = f2 (x) for every x in U1 U2 . Prove that f (x) = is a smooth f
CSU Northridge - MATH - 550
Math 550. Homework 2 (Revised). Due 9/22/2003Problem 1 Let U be the union of two open sets U1 ,U2 , i.e., U = U1 U2 . Let f j be a smooth functions on U j , j = 1, 2, such that f1 (x) = f2 (x) for every x in U1 U2 . Prove that f (x) = is a smooth f
CSU Northridge - MATH - 53971
Math 550. Homework 1. Due 9/3/2003Problem 1 Let U be an open subset of the plane. Prove that U is connected if and only if every locally constant function on U is constant on U . Problem 2 Let = ydx xdy and let be the line segment from (0, 0) to
CSU Northridge - MATH - 550
Math 550. Homework 1. Due 9/3/2003Problem 1 Let U be an open subset of the plane. Prove that U is connected if and only if every locally constant function on U is constant on U . Problem 2 Let = ydx xdy and let be the line segment from (0, 0) to
CSU Northridge - MATH - 53971
Math 550. Homework 6. Due 10/22/03Denition 1. Two continuous mappings f , g : X Y are homotopic if there is a continuous mapping H : X [0, 1] Y such that H(x, 0) = f (x) and H(x, 1) = g(x) for all x in X. Problem 1. Let C and C be circles. (i) P
CSU Northridge - MATH - 550
Math 550. Homework 6. Due 10/22/03Denition 1. Two continuous mappings f , g : X Y are homotopic if there is a continuous mapping H : X [0, 1] Y such that H(x, 0) = f (x) and H(x, 1) = g(x) for all x in X. Problem 1. Let C and C be circles. (i) P
CSU Northridge - MATH - 53971
Math 550. Homework 5. Due 10/15/03Problem 1. Let : [a, b] R2 \ {0} be a continuous path. Prove that there are continuous functions r : [a, b] R+ (the positive real numbers) and : [a, b] R, so that (t) = (r(t) cos (t), r(t) sin (t), a t b.P
CSU Northridge - MATH - 550
Math 550. Homework 5. Due 10/15/03Problem 1. Let : [a, b] R2 \ {0} be a continuous path. Prove that there are continuous functions r : [a, b] R+ (the positive real numbers) and : [a, b] R, so that (t) = (r(t) cos (t), r(t) sin (t), a t b.P
CSU Northridge - MATH - 53971
Math 550. Homework 4. Due 10/01/2003Problem 1 Given a 1-form on an open set U, prove that the following are equivalent (i) d = 0; (ii)R R = 0 for all closed rectangles R contained in U; (iii) every point in U has a neighborhood such that = 0 f
CSU Northridge - MATH - 550
Math 550. Homework 4. Due 10/01/2003Problem 1 Given a 1-form on an open set U, prove that the following are equivalent (i) d = 0; (ii)R R = 0 for all closed rectangles R contained in U; (iii) every point in U has a neighborhood such that = 0 f
CSU Northridge - MATH - 53971
Math 550. Homework 3. Due 9/24/2003You have two options to choose from. Option A Generalize (that is, state and prove) the last lemma proved in class today (9/10) to an open set of the form U = R2 \ {P1 , , Pn }. Option B Prepare a set of lectur
CSU Northridge - MATH - 550
Math 550. Homework 3. Due 9/24/2003You have two options to choose from. Option A Generalize (that is, state and prove) the last lemma proved in class today (9/10) to an open set of the form U = R2 \ {P1 , , Pn }. Option B Prepare a set of lectur
CSU Northridge - MATH - 512
Math 512B. Homework 1. Due 1/30/08(Revised 1/27)Problem 1. In class we dened cos x and sin x for x in [0, ]. The values of cos x and sin x for x not in [0, ] are dened in two steps as follows: (1) If x 2, then set cos x sin x = cos(2 x), = sin
CSU Northridge - MATH - 53971
Math 512B. Homework 1. Due 1/30/08(Revised 1/27)Problem 1. In class we dened cos x and sin x for x in [0, ]. The values of cos x and sin x for x not in [0, ] are dened in two steps as follows: (1) If x 2, then set cos x sin x = cos(2 x), = sin
CSU Northridge - MATH - 512
Math 512B. Homework 3. Due 2/13/08The symbol lim f (x) means the limit of f (x) as x approaches . We say that lim f (x) = L if for every x x > 0 there is a number M such that, for all x, if x > M , then |f (x) L| < . A similar denition applies t
CSU Northridge - MATH - 53971
Math 512B. Homework 3. Due 2/13/08The symbol lim f (x) means the limit of f (x) as x approaches . We say that lim f (x) = L if for every x x > 0 there is a number M such that, for all x, if x > M , then |f (x) L| < . A similar denition applies t
CSU Northridge - MATH - 512
Math 512B. Homework 4. Due 2/20/08(Revised 2/18)Problem 1. (i) Prove that the remainder R2n+1,0,arctan (x) of degree 2n + 1 of the function arctan satises |R2n+1,0,arctan (x)| for |x| 1. (ii) Use the relation arctan x + arctan y = arctan x+y 1 x
CSU Northridge - MATH - 53971
Math 512B. Homework 4. Due 2/20/08(Revised 2/18)Problem 1. (i) Prove that the remainder R2n+1,0,arctan (x) of degree 2n + 1 of the function arctan satises |R2n+1,0,arctan (x)| for |x| 1. (ii) Use the relation arctan x + arctan y = arctan x+y 1 x
CSU Northridge - MATH - 512
Math 512B. Homework 9. Due 4/37/08Problem 1. Let z1 , z2 , z3 be three distinct nonzero complex numbers. Prove that the following are equivalent: (i) The points z1 , z2 , and z3 are the vertices of an equilateral triangle. (ii) The center of mass o
CSU Northridge - MATH - 53971
Math 512B. Homework 9. Due 4/37/08Problem 1. Let z1 , z2 , z3 be three distinct nonzero complex numbers. Prove that the following are equivalent: (i) The points z1 , z2 , and z3 are the vertices of an equilateral triangle. (ii) The center of mass o
CSU Northridge - MATH - 512
Math 512B. Homework 8. Due 4/16/08Problem 1. (i) Find the Fourier series of the following functions (they are 2-periodic, so only the values on (, ] are given). (a) f (x) = 0 if < x 0 and f (x) = sin x if 0 < x . (b) g(x) = x2 if < x . (ii) Di
CSU Northridge - MATH - 53971
Math 512B. Homework 8. Due 4/16/08Problem 1. (i) Find the Fourier series of the following functions (they are 2-periodic, so only the values on (, ] are given). (a) f (x) = 0 if < x 0 and f (x) = sin x if 0 < x . (b) g(x) = x2 if < x . (ii) Di
CSU Northridge - ICH - 530
Chondrichthyes: Cartilaginous FishesI. Chondrichthian characteristics & groupsReviewSuperclass Gnathostomata - Jawed fishes Class Placodermi (plate-skinned) Class Acanthodii (spiny sharks) extinct extinctII. Holocephali III. Elasmobranchii A
CSU Northridge - ICH - 530
SwimmingI. Types of swimming II. Methods for generating propulsion III. Forces resisting movement IV. Adaptations to different swimming modes V. Relationships between swimming and ecologyFishes swim in lots of different ways. I. Types of swimming
CSU Northridge - ICH - 530
I. Lifetime spawning frequency Reproduction in FishesI. Lifetime spawning frequency II. Spawning cycles III. Modes of spawning IV. Sex change and mating systemsSemelparity spawn once Iteroparity spawn multiple times semelparous iteroparousWhy?
CSU Northridge - JMK - 7693
Norm Herr Types of Graphs Causes of Death in California, 2000 diseases of heart 68,533 malignant neoplasms 53,005 cerebrovascular diseases 18,090 chronic respiratory diseases 12,754 accidents 8,814 influenza & pneumonia 8,355 diabetes 6,203 alzheimer
CSU Northridge - JMK - 7693