CALC II
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58 Terms
Area between two graphs (Vertically simple)
Area between two graphs (Horiontally simple)
Total Mass
Average Value
Volume using Disk Method
The solid obtained by rotating the region under the graph about the x-axis has volume
Volume using Washer Method
Volume using Shell Method
Integration by Parts
sin2x
cos2x
d/dx (sin-1f(x))
d/dx (cos-1f(x))
d/dx (tan-1f(x))
Half-life and Doubling Time
Exponential decay: Half-life
k < 0
Exponential growth: Doubling-time
k > 0
Indeterminate forms (take l’Hopital)
Geometric Series
Sum of Geometric Series when | r | < 1
Geometric Series: Converges to 0
| r | < 1
Geometric Series: Converges to c
r = 1
Geometric Series: Diverges
Sum of a Geometric Series
nth Divergence Test
Integral Test
Must be positive, decreasing, and continuous
p-Series Test
Direct Comparison Test
Limit Comparison Test when L > 0
Must be positive sequences
Limit Comparison Test when L = 0
Must be positive sequences
Limit Comparison Test when L = ♾
Must be positive sequences
Alternating Series Test
Take derivative to prove that the sequence is decreasing
Alternating Series Estimation
The error approximating S by SN is less than the next term in the series
Ratio Test when ρ < 1
Absolutely Convergent
Ratio Test when ρ > 1
Divergent
Ratio Test when ρ = 1
Inconclusive → use other test
Root Test when L < 1
Absolutely Convergent
Root Test when L > 1
Divergent
Root Test when L = 1
Inconclusive → use other test
Power Series with a Center c
Maclaurin Series of ex
Maclaurin Series of sinx
Maclaurin Series of cosx
Maclaurin Series of 1/(1-x)
Maclaurin Series of 1/(1+x)
Maclaurin Series of ln (1+x)
Maclaurin Series of arctanx
Binomial Series (1+x)a
Parameterization of a Line: The line through P=(a,b) of slope m is parametrized by
Parameterization of a Circle with radius R and centered at (a,b)
Parameterization of an Ellipse
Slope of Tangent Line ~ Parametric Curve
Arc Length
Speed Along a Parametrized Path
Area in Polar Coordinates
Arc Length in Polar Coordinates
polar equation of the line L whose point closest to the origin is Po=(d,𝛼)
