Study Guide - Test 2 (MATH-2212, Spring-2017).pdf -...

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MATH-2212: Calculus of One Variable IIStudy Guide for Test 2, Spring 2017Study Guide for Test 2It goes without saying that mathematics develops cumulatively, and all subsequent topics usuallydepend heavily on some (if not all) previous material. This study guide is intended to emphasizethe new material learned in this portion of the course. Knowing and understanding everything thathas been covered before — in prerequisite courses and earlier in this course — is also crucial forsuccess on this test.Test ContentsSection 7.8– Improper IntegralsSection 8.1– Arc LengthSection 10.1– Curves Defined by Parametric EquationsSection 10.2– Calculus with Parametric CurvesSection 10.3– Polar CoordinatesSection 10.4– Areas and Lengths in Polar CoordinatesSection 11.1– SequencesKey ConceptsImproper integrals; convergence and divergence of improper integrals.Polar coordinates; conversion between polar and cartesian coordinates; sketching graphs ofequations in polar coordinates.Parametric equations and curves; converting parametric equations to cartesian equations byeliminating the parameter; graphs of curves given parametrically.Arc length of a curve; finding the arc length of curves given by explicit functions, parametricequations, or polar equations.Equations of tangent lines to parametrically defined curves.Area under a curve defined by parametric equations.Areas enclosed by polar curves.– 1–
MATH-2212: Calculus of One Variable IIStudy Guide for Test 2, Spring 2017Sequences of real numbers; sequence notation; common term formulas for sequences; mono-tonic sequences.The limit of a sequence (intuitively); convergent and divergent sequences; relationships amongconvergence, boundedness, and monotonicity properties.Some special limit formulas.Some Important Definitions, Formulas, and PropertiesConversion Formulas Between Polar and Cartesian Coordinatesx=rcosθr2=x2+y2y=rsinθtanθ=yxDerivatives and Tangent Lines to Parametric CurvesFor a parametrically defined curvex=x(t),y=y(t), the derivative ofyas a function ofxcan be found asdydx=dy/dtdx/dt, provideddydx6= 0.An equation of the tangent line to the graph of a parametrically defined curvex=x(t),y=y(t) at a pointt0, i.e at a point (x0=x(t0), y0=y(t0)), can be set up asy-y0=dydxt=t0·(x-x0), provideddydxt=t06

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