153 Equation Sheet - Ch 10 Tangent of Parametric Curves(661 Arc Length Tangents to Polar Curves(674 Area(680 Arc Length Ch 11 Limits of Sequences(703 If

153 Equation Sheet - Ch 10 Tangent of Parametric Curves(661...

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Ch 10Tangent of Parametric Curves (661):=dydxdydtdxdtArc Length:= +Lt1t2dxdt2 dydt2 dtTangents to Polar Curves (674):=+ - dydxdrdθsinθ r cosθdrdθcosθ r sinθArea (680): = Aθ1θ212r2 dθArc Length:= + Lθ1θ2r2drdθ2Ch 11Limits of Sequences (703): If a sequence has a limit that exists as it approaches infinity, then it converges.Geometric Series (715): = ∞-=- , <n1arn 1a1 rr 1P-Series (725): = ∞n11npis convergent if p>1, divergent if p1Integral Test (724): If 1fxdxconverges, then = ∞n1anconverges Comparison Test (731):
If bnis convergent and anbnfor all n, then anconvergesIf bnis divergent and anbnfor all n, then andivergesLimit Comparison Test (733):If →∞limnanbn= C and C>0 then either both series converge or divergeAlternating Series Test (736):= ∞--n11n 1bnis convergent if it is decreasing and →∞=limnbn0Root Test (744): If →∞limnnan= L < 1, the series is absolutely convergent, if L <1 or