Multivariate Functions and Their Graphs / Cylindrical and Spherical Coordinates /Ĭhapter 43 DIRECTIONAL DERIVATIVES AND THE GRADIENT. LINES AND PLANESĬhapter 41 FUNCTIONS OF SEVERAL VARIABLES Parametric Equations of Plane Curves / Vector-Valued Functions /Ĭhapter 40 VECTORS IN SPACE. Surface Area of a Solid of Revolution / Work / Centroid of a Planar Region /Ĭhapter 34 PARAMETRIC EQUATIONS, VECTOR FUNCTIONS, CURVILINEAR MOTION Used thus, 3000 Solved Problems in Calculus can almost serve as a supplement to any course in calculus, or even as an independent refresher course.Ĭhapter 10 TRIGONOMETRIC FUNCTIONS AND THEIR DERIVATIVESĬhapter 11 ROLLE’S THEOREM, THE MEAN VALUE THEOREM, AND THE SIGN OF THE DERIVATIVEĬhapter 12 HIGHER-ORDER DERIVATIVES AND IMPLICIT DIFFERENTIATIONĬhapter 16 APPLIED MAXIMUM AND MINIMUM PROBLEMSĬhapter 18 APPROXIMATION BY DIFFERENTIALSĬhapter 19 ANTIDERIVATIVES (INDEFINITE INTEGRALS)Ĭhapter 20 THE DEFINITE INTEGRAL AND THE FUNDAMENTAL THEOREM OF CALCULUSĬhapter 27 INVERSE TRIGONOMETRIC FUNCTIONSĬhapter 29 TRIGONOMETRIC INTEGRANDS AND SUBSTITUTIONSĬhapter 30 INTEGRATION OF RATIONAL FUNCTIONS: THE METHOD OF PARTIAL FRACTIONSĬhapter 31 INTEGRALS FOR SURFACE AREA, WORK, CENTROIDS You might even disdain to read it until, with pencil and paper, you have solved the problem yourself (or failed gloriously). You might wish to delay consulting that solution until you have outlined an attack in your own mind. The printed solution that immediately follows a problem statement gives you all the details of one way to solve the problem. Our ordering of the chapters follows the customary order found in many textbooks, but as no two textbooks have exactly the same sequence of topics, you must expect an occasional discrepancy from the order followed in your course. It is assumed that you have available a calculus textbook, including tables for the trigonometric, logarithmic, and exponential functions. Their difficulty usually increases as the chapter progresses, but there is no uniform pattern. We have aimed at presenting the broadest range of problems that you are likely to encounter-the old chestnuts, all the current standard types, and some not so standard.Įach chapter begins with very elementary problems. This collection of solved problems covers elementary and intermediate calculus, and much of advanced calculus.
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