TAILIEUCHUNG - Ebook Calculus early transcendental functions (6th edition): Part 2

(BQ) Part 2 book "Calculus early transcendental functions" has contents: Conics, parametric equations, and polar coordinates; vectors and the geometry of space; vector valued functions; functions of several variables; multiple integration; vector analysis. | 680 Chapter 9 Infinite Series 8. Using the Alternating Series Test function Ά 1, f ͑x͒ ϭ sin x , x The graph of the 13. Deriving Identities Derive each identity using the appropriate geometric series. (a) 1 ϭ . . . (b) xϭ0 1 ϭ . . . x > 0 is shown below. Use the Alternating Series Test to show that the improper integral ͵ ϱ 1 f ͑x͒ dx converges. y 1 π 2π 3π 14. Population Consider an idealized population with the characteristic that each member of the population produces one offspring at the end of every time period. Each member has a life span of three time periods and the population begins with 10 newborn members. The following table shows the population during the first five time periods. x 4π Time Period Age Bracket 1 2 3 4 5 0–1 10 10 20 40 70 10 10 20 40 10 10 20 40 70 130 −1 9. Conditional and Absolute Convergence For what values of the positive constants a and b does the following series converge absolutely? For what values does it converge conditionally? b a b a b a b . . . ϩ Ϫ ϩ Ϫ ϩ Ϫ ϩ 2 3 4 5 6 7 8 2–3 Total 10 20 The sequence for the total population has the property that Sn ϭ SnϪ1 ϩ SnϪ2 ϩ SnϪ3, n > 3. Find the total population during each of the next five time periods. 10. Proof (a) Consider the following sequence of numbers defined recursively. a1 ϭ 3 a2 ϭ Ί3 a3 ϭ Ί3 ϩ Ί3 15. Spheres Imagine you are stacking an infinite number of spheres of decreasing radii on top of each other, as shown in the figure. The radii of the spheres are 1 meter, 1͞Ί2 meter, 1͞Ί3 meter, and so on. The spheres are made of a material that weighs 1 newton per cubic meter. (a) How high is this infinite stack of spheres? Ӈ (b) What is the total surface area of all the spheres in the stack? anϩ1 ϭ Ί3 ϩ an Write the decimal approximations for the first six terms of this sequence. Prove that the sequence converges, and find its limit. (c) Show that the weight of the .

• Toán học
• Calculus early transcendental functions
• Transcendental functions
• Parametric equations
• Polar coordinates
• Vector valued functions
• Several variables
• Preparation for calculus
• Their properties
• Integration techniques
• Partial fractions
• Trigonometric integrals
• Fixed point
• Linear equations in several variables
• Quasi normed space
• Several variables in quasi normed spaces
• Generalized linear equations
• Analytic functions
• Linear k positive operators
• Korovkin type theorems
• Complex variables
• Uniqueness problem
• Meromorphic functions
• Difference operators
• Several complex variables
• The plane integral
• space integral
• line integral
• surface integral
• Semi polar coordinates
• Gradient
• Directional derivative
• Partial derivatives
• The chain rule
• higher order
• Tangents to curves
• Tangent plane to a surface
• Simple integrals
• Extremum
• Extrema
• Rule of Four
• Functions and change
• Exponential functions
• Functions os several variables
• A fundamental tool
• Differentiating functions of several variables
• báo cáo của tạp chí Journal of Operator Theory
• tài liệu báo cáo nghiện cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• trigonometric polynomials
• Calculation
• Approximating polynomials
• Gradient fields
• Rectangular coordinates
• Maximum and minimum
• Spherical coordinates
• Point Sets
• Examinations of functions
• Level curves
• level surfaces
• Conics
• Continuous functions
• Description of curves
• Connected sets
• Space integrals
• Volume
• Moment of inertia
• centre of gravity
• Improper space integrals
• Line integrals
• Arc lengths
• parametric descriptions
• Tangential line integrals
• Gradient elds
• integrals
• vector eld
• divergence
• rotation
• Gauβ’s theorem
• Stokes’s theorem
• Nabla calculus
• Vector potentials
• Green’s identities
• Curvilinear coordinates
• m Electromagnetism
• Miscellaneous
• chain rule
• plane integral
• antiderivatives
• tài liệu báo cáo nghiên cứu khoa học
• công trình toán học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• Functions of Several variables
• Toán ứng dụng
• Toán cao cấp
• Calculus and its applications
• Công thức toán học
• Đại số giới hạn
• Fundamentals of calculus
• Integral calculus
• Techniques of integration
• Series and summations
• Applications to probability
• Marginal functions
• Comparative statics
• Partial elasticity
• Natural logarithm functions
• Economic functions
• Olive oil market volatility
• GARCH techniques
• ARCH techniques
• Several explanatory variables
• Business decisions