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1The Elements Of The Integral Calculus: With Its Applications To Geometry And ...

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2The Elements Of The Integral Calculus; With Its Applications To Geometry And To The Summation Of Infinite Series. Intended For The Use Of Mathematical Students In Schools And Universities

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3Ricci-Calculus: An Introduction To Tensor Analysis And Its Geometrical Applications

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4Calculus And Its Applications: Expanded Version

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5The Elements Of The Integral Calculus: With Its Applications To Geometry And ...

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6NASA Technical Reports Server (NTRS) 19810004275: Development Of Boolean Calculus And Its Applications. [digital Systems Design

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The development of Boolean calculus for its application to developing digital system design methodologies that would reduce system complexity, size, cost, speed, power requirements, etc., is discussed. Synthesis procedures for logic circuits are examined particularly asynchronous circuits using clock triggered flip flops.

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7Stochastic Calculus Of Variations For General Lévy Processes And Its Applications To Jump-type SDE's With Non-degenerated Drift

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We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of the noise, and this is the main difference between our method and the known methods by J.Bismut or J.Picard. The main tool in our approach is the stochastic calculus of variations for a L\'evy process, based on the time-stretching transformations of the trajectories. Three problems are solved in this framework. First, we prove that if the drift coefficient a is non-degenerated in an appropriate sense, then the law of the solution to the Cauchy problem for the initial equation is absolutely continuous, as soon as the L\'evy measure of the noise satisfies one of the rather weak intensity conditions, for instance the so-called wide cone condition. Secondly, we provide the sufficient conditions for the density of the distribution of the solution to the Cauchy problem to be smooth in the terms of the family of the so-called order indices of the L\'evy measure of the noise (the drift again is supposed to be non-degenerated). At last, we show that an invariant distribution to the initial equation, if exists, possesses a C^\infty-density provided the drift is non-degenerated and the L\'evy measure of the noise satisfies the wide cone condition.

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8Brief Calculus And Its Applications

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Includes index

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9A Treatise On The Integral Calculus And Its Applications With Numerous Examples

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10Clone Theory: Its Syntax And Semantics, Applications To Universal Algebra, Lambda Calculus And Algebraic Logic

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The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this purpose are various clones over a full subcategory of a category. We show that the syntax of equational logic, lambda calculus and first order logic can be represented as clones or right algebras of clones over the set of positive integers. The semantics is then represented by structures derived from left algebras of these clones.

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11Some Basic Properties Of G-Calculus And Its Applications In Numerical Analysis

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Objective of this paper is to introduce a new type of calculus which will be called G-Calculus based on non-Newtonian calculus introduced by Grossman and Katz \cite{GrossmanKatz}. The basic difference between geometric calculus defined by Grossman and Katz and the present G-calculus is that Grossman took the values of the argument as $x, x+ h, x+2h,...$ but here in G-calculus we take the values as $x, x\oplus h, x\oplus e^2\odot h, x\oplus e^3\odot h....$ This calculus will have great deal with numerical analysis which are discussed in the last section of this paper.

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12Instructor's Solutions Manual For CALCULUS And ITS APPLICATIONS By Bittenger, Ellenbogen

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Objective of this paper is to introduce a new type of calculus which will be called G-Calculus based on non-Newtonian calculus introduced by Grossman and Katz \cite{GrossmanKatz}. The basic difference between geometric calculus defined by Grossman and Katz and the present G-calculus is that Grossman took the values of the argument as $x, x+ h, x+2h,...$ but here in G-calculus we take the values as $x, x\oplus h, x\oplus e^2\odot h, x\oplus e^3\odot h....$ This calculus will have great deal with numerical analysis which are discussed in the last section of this paper.

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13The Elements Of The Integral Calculus: With Its Applications To Geometry And ...

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14A Treatise On The Integral Calculus And Its Applications: With Numerous Examples

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15Study Guide And Selected Solutions : Brief Calculus And Its Applications

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16A Treatise On The Integral Calculus And Its Applications With Numerous Examples

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17A Treatise On The Integral Calculus And Its Applications

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18ERIC ED218131: Curve Fitting Via The Criterion Of Least Squares. Applications Of Algebra And Elementary Calculus To Curve Fitting. [and] Linear Programming In Two Dimensions: I. Applications Of High School Algebra To Operations Research. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 321, 453.

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This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to do desired curve fitting; and 5) use augmented matrix approach to solve simultaneous equations. The second unit provides techniques to formulate simple linear programing problems and solve them graphically. Both modules contain exercises and provide exams. Answers to all problems are supplied. (MP)

“ERIC ED218131: Curve Fitting Via The Criterion Of Least Squares. Applications Of Algebra And Elementary Calculus To Curve Fitting. [and] Linear Programming In Two Dimensions: I. Applications Of High School Algebra To Operations Research. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 321, 453.” Metadata:

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“ERIC ED218131: Curve Fitting Via The Criterion Of Least Squares. Applications Of Algebra And Elementary Calculus To Curve Fitting. [and] Linear Programming In Two Dimensions: I. Applications Of High School Algebra To Operations Research. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 321, 453.” Subjects and Themes:

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19Calculus And Its Applications

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This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to do desired curve fitting; and 5) use augmented matrix approach to solve simultaneous equations. The second unit provides techniques to formulate simple linear programing problems and solve them graphically. Both modules contain exercises and provide exams. Answers to all problems are supplied. (MP)

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20Ricci-calculus An Introduction To Tensor Analysis And Its Geometrical Applications

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This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to do desired curve fitting; and 5) use augmented matrix approach to solve simultaneous equations. The second unit provides techniques to formulate simple linear programing problems and solve them graphically. Both modules contain exercises and provide exams. Answers to all problems are supplied. (MP)

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21Calculus And Its Applications

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This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to do desired curve fitting; and 5) use augmented matrix approach to solve simultaneous equations. The second unit provides techniques to formulate simple linear programing problems and solve them graphically. Both modules contain exercises and provide exams. Answers to all problems are supplied. (MP)

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22Calculus And Its Applications

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This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to do desired curve fitting; and 5) use augmented matrix approach to solve simultaneous equations. The second unit provides techniques to formulate simple linear programing problems and solve them graphically. Both modules contain exercises and provide exams. Answers to all problems are supplied. (MP)

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23Calculus And Its Applications

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This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to do desired curve fitting; and 5) use augmented matrix approach to solve simultaneous equations. The second unit provides techniques to formulate simple linear programing problems and solve them graphically. Both modules contain exercises and provide exams. Answers to all problems are supplied. (MP)

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24The Elements Of The Integral Calculus: With Its Applications To Geometry And ...

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25Calculus And Its Applications

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26A Treatise On The Differential Calculus, And Its Applications To Algebra And Geometry, Founded On The Method Of Infinitesimals

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27The Elements Of The Integral Calculus: With Its Applications To Geometry And ...

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28A Treatise On Advanced Calculus, Including Those Parts Of The Theory Of Functions Of Real And Complex Variables Which Form The Logical Basis Of The Infinitesimal Analysis And Its Applications To Geometry And Physics

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595 pages

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29Advanced Calculus And Its Applications To The Engineering And Physical Sciences

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595 pages

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30A Text-book Of Mathematical Analysis : The Uniform Calculus And Its Applications

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475 p

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31Calculus And Its Applications Custom Edition For Salt Lake Community College

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475 p

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32A Treatise On The Integral Calculus And Its Applications: With Numerous Examples

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33Practical Treatise On The Differential And Integral Calculus, With Some Of Its Applications To Mechanics And Astronomy

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208 p. 20 cm

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34Fractional Calculus And Its Applications : Proceedings Of The International Conference Held At The University Of New Haven, June, 1974

208 p. 20 cm

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35Mathematics With Calculus : And Its Applications To Management, Life, And Social Sciences

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208 p. 20 cm

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36ERIC ED218104: Price Discrimination And Consumer Surplus. Applications Of Calculus To Economics Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Unit 294.

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This unit considers the application of calculus in determining price discrimination and consumer surplus in a competitive market. Producer surplus and two-tier price discrimination are also developed in problems. It is noted that calculus cannot usually provide numerical answers for practical economic problems. The importance of calculus applications is seen to be in the contributions made to the development of economic theory. It is felt that the examples developed can provide insight into the theoretical relationships in economics and how calculus is used in their development. Exercises and a model exam are included, with answers provided to both at the end of the material. (MP)

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37Vector Calculus In Non-Integer Dimensional Space And Its Applications To Fractal Media

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We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

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38Introduction To The Calculus Of Variations And Its Applications

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We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

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39Practical Treatise On The Differential And Integral Calculus With Some Of Its Applications To Mechanics And Astronomy

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40Differential Calculus And Its Applications

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41A Treatise On The Integral Calculus And Its Applications With Numerous Examples

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42Generalized Pathway Entropy And Its Applications In Diffusion Entropy Analysis And Fractional Calculus

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We presented background information about various entropies in the literature. The pathway idea of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure and established connections to outstanding problems in astronomy and physics. In this paper we proved that the generalized entropy of Mathai associated with diffusive processes grows linearly with the logarithm of time, and the rate of growth is indepen- dent of the generalized entropy parameter. We also proposed some results concerning images of generalized Bessel function under the pathway operator and its special cases including some trigonometric functions. Situations are listed where a generalized entropy of order ? leads to pathway models, exponential and power law behavior and related differential equations.

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43A Treatise On The Integral Calculus And Its Applications With Numerous ...

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44Study Guide With Selected Solutions : Brief Calculus And Its Applications

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[vii], 240 pages : 26 cm

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45The Elements Of The Integral Calculus: With Its Applications To Geometry And To The Summation Of ...

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46Calculus And Its Applications 2nd

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47Student's Solutions Manual : Calculus & Its Applications, Twelfth Edition, And Brief Calculus & Its Applications, Twelfth Edition, Larry J. Goldstein [and Others]

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48ERIC ED218132: Developing The Fundamental Theorem Of Calculus. Applications Of Calculus To Work, Area, And Distance Problems. [and] Atmospheric Pressure In Relation To Height And Temperature. Applications Of Calculus To Atmospheric Pressure. [and] The Gradient And Some Of Its Applications. Applications Of Multivariate Calculus To Physics. [and] Kepler's Laws And The Inverse Square Law. Applications Of Calculus To Physics. UMAP Units 323, 426, 431, 473.

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This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views calculus applications to atmospheric pressure. The material is geared to aid pupil understanding of the application of calculus to construct a mathematical model of the atmosphere. The third unit covers applications of multivariate calculus to physics. The user is expected to learn how to compute the Gradient, and to be able to use the Gradient to solve certain practical problems involving steepest ascent. The final module covers calculus applications to physics. The material is designed to instruct pupils how to: 1) be able to handle motion problems in polar coordinates, especially those concerning gravitational interaction; 2) state the relationships between Kepler's Laws and the Inverse Square Law; and 3) discuss the history and thought going into scientific development of an idea and the interaction between experiment and theory, at least in the context of planetary motion. All units include exercises with solutions; the first, third, and fourth provide model exams with answers. (MP)

“ERIC ED218132: Developing The Fundamental Theorem Of Calculus. Applications Of Calculus To Work, Area, And Distance Problems. [and] Atmospheric Pressure In Relation To Height And Temperature. Applications Of Calculus To Atmospheric Pressure. [and] The Gradient And Some Of Its Applications. Applications Of Multivariate Calculus To Physics. [and] Kepler's Laws And The Inverse Square Law. Applications Of Calculus To Physics. UMAP Units 323, 426, 431, 473.” Metadata:

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  • Language: English

“ERIC ED218132: Developing The Fundamental Theorem Of Calculus. Applications Of Calculus To Work, Area, And Distance Problems. [and] Atmospheric Pressure In Relation To Height And Temperature. Applications Of Calculus To Atmospheric Pressure. [and] The Gradient And Some Of Its Applications. Applications Of Multivariate Calculus To Physics. [and] Kepler's Laws And The Inverse Square Law. Applications Of Calculus To Physics. UMAP Units 323, 426, 431, 473.” Subjects and Themes:

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49Calculus And Its Applications

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This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views calculus applications to atmospheric pressure. The material is geared to aid pupil understanding of the application of calculus to construct a mathematical model of the atmosphere. The third unit covers applications of multivariate calculus to physics. The user is expected to learn how to compute the Gradient, and to be able to use the Gradient to solve certain practical problems involving steepest ascent. The final module covers calculus applications to physics. The material is designed to instruct pupils how to: 1) be able to handle motion problems in polar coordinates, especially those concerning gravitational interaction; 2) state the relationships between Kepler's Laws and the Inverse Square Law; and 3) discuss the history and thought going into scientific development of an idea and the interaction between experiment and theory, at least in the context of planetary motion. All units include exercises with solutions; the first, third, and fourth provide model exams with answers. (MP)

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50Calculus And Its Applications

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This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views calculus applications to atmospheric pressure. The material is geared to aid pupil understanding of the application of calculus to construct a mathematical model of the atmosphere. The third unit covers applications of multivariate calculus to physics. The user is expected to learn how to compute the Gradient, and to be able to use the Gradient to solve certain practical problems involving steepest ascent. The final module covers calculus applications to physics. The material is designed to instruct pupils how to: 1) be able to handle motion problems in polar coordinates, especially those concerning gravitational interaction; 2) state the relationships between Kepler's Laws and the Inverse Square Law; and 3) discuss the history and thought going into scientific development of an idea and the interaction between experiment and theory, at least in the context of planetary motion. All units include exercises with solutions; the first, third, and fourth provide model exams with answers. (MP)

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