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Case 1 x: xx 3 11 2 3 x 3 22 x x 5 which is never true if 1 x, so no solution here. Thomas - calculus and solutions to exercises 11th edition The standard textbook used in our institute to teach calculus in freshman year. to get access to your one-sheeter, Limits at Infinity; End Behaviour of a Function, Introduction of Techniques of Differentiation, Local Linear Approximation; Differentials, Analysis of Functions I: Increase, Decrease, and Concavity, Analysis of Functions II: Relative Extrema; Graphing Polynomials, Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents, The Definition of Area as a Limit; Sigma Notation, Rectilinear Motion Revisited Using Integration, Average Value of a Function and its Applications, Evaluating Definite Integrals by Substitution, Moments, Centers of Gravity, and Centroids, Derivatives and Integrals Involving Logarithmic Functions, Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions, Graphs and Applications Involving Logarithmic and Exponential Functions, Logarithmic and Other Functions Defined by Integrals, Derivatives and Integrals Involving Inverse Trigonometric Functions, Integrating Rational Functions by Partial Fractions, Using Computer Algebra Systems and Tables of Integrals, First-Order Differential Equations and Applications, Alternating Series; Absolute and Conditional Convergence, Maclaurin and Taylor Series; Power Series, Differentiating and Integrating Power Series; Modeling with Taylor Series, Parametric Equations; Tangent Lines and Arc Length for Parametric Curves, Tangent Lines, Arc Length, and Area for Polar Curves, Rotation of Axes; Second-Degree Equations, Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces, Unit Tangent, Normal, and Binormal Vectors, Differentiability, Differentials, and Local Linearity, Maxima and Minima of Functions of Two Variables, Double Integrals Over Non Rectangular Regions, Triple Integrals in Cylindrical and Spherical Coordinates, Change of Variables in Multiple Integrals; Jacobians, Centers of Gravity Using Multiple Integrals, Independence of Path; Conservative Vector Fields. 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