TOPICS FOR FINAL EXAM
Integration: substitution method, trigonometric substitutions
integration by parts
partial fractions
improper integrals.
Applications: areas between curves
volumes (washer, cylindrical shells, slicing)
arc length
work.
Sequences: limits
monotone sequences.
Series: geometric series
p-series
divergence test
alternating series
conditional convergence
absolute convergence
ratio test
root test.
Power series: Radius of convergence
interval of convergence
Taylor series
integration of series, differentiation of series.
Parametric equations: circles, lines
tangents to a curve
arc length
area under a curve.
Polar equations: circles
lines
spirals
n-petal roses
lemniscates
cardioids
lima¸cons
areas of regions bounded by curves given by polar equations.
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