153 Equation Sheet

153 Equation Sheet - then the series is divergent, if L= 1...

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Ch 10 Tangent of Parametric Curves (661): = dydx dydtdxdt Arc Length: = + L t1t2dxdt2 dydt2 dt Tangents to Polar Curves (674): = + - dydx drdθsinθ r cosθdrdθcosθ r sinθ Area (680): = A θ1θ212r2 dθ Arc Length: = + L θ1θ2r2 drdθ2 dθ Ch 11 Limits of Sequences (703): If a sequence has a limit that exists as it approaches infinity, then it converges. Geometric Series (715): = ∞ - = - , < n 1 arn 1 a1 r r 1 P-Series (725): = ∞ n 1 1np is convergent if p>1, divergent if p 1 Integral Test (724): If 1 fxdx converges, then = ∞ n 1 an converges Comparison Test (731):
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If bn is convergent and an bn for all n, then an converges If bn is divergent and an bn for all n, then an diverges Lim it Comparison Test (733): If →∞ limn anbn = C and C> 0 then either both series converge or diverge Alternating Series Test (736): = ∞- - n 1 1n 1bn is convergent if it is decreasing and →∞ = limn bn 0 Root Test (744): If →∞ limn nan = L < 1, the series is absolutely convergent, if L <1 or
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Unformatted text preview: then the series is divergent, if L= 1 the test is inconclusive Ratio Test (742): If + limn an 1an = L &lt; 1, the series is absolutely convergent, if L &lt;1 or then the series is divergent, if L= 1 the test is inconclusive Absolute and Conditional Convergence (740): If the absolute value of a series converges, the series is absolutely convergent, if the series converges, but the absolute value of the series doesnt the series is conditionally convergent. Radius and Interval of Convergence (751): | x-a |&lt; R, where R is the radius of convergence, and the interval of convergence is the interval for which the series converges Integration and Differentiation of a Power Series (755): = =- n 0 xn 11 x = =-ddxn 0 xn ddx11 x = = - =-n 0 nxn 1 11 x2 = =-n 0 xn 11 x Taylor and Maclurin Series (761):...
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153 Equation Sheet - then the series is divergent, if L= 1...

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