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Evaluate integrals using basic integration techniques
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
select the basic integration formula to use for evaluating a given integral
evaluate integrals using substitution
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Evaluate integrals using advanced integration techniques
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
evaluate integrals using integration by parts
evaluate integrals involving powers of trigonometric functions
evaluate integrals by trigonometric substitution
evaluate integrals by use partial fraction decomposition
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Analyze infinite sequences
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
identify the nth term of a sequence
determine whether an infinite sequence is convergent or divergent
find the limit of a convergent sequence
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Analyze power series
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
find the interval of convergence of a power series
find Taylor series of elementary functions
find the Taylor Series of an analytic function centered at a given x-value
use Taylor series to solve application problems
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Analyze first-order differential equations
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
verify that a function satisfies a differential equation
use the direction field to sketch the graph of the solutions of a differential equation
solve separable first-order differential equations
use separable differential equations to solve application problems
use integrating factors to solve linear first-order linear differential equations
use first-order linear differential equations to solve application problems
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Explore vectors
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
find the position vector of a point
find the magnitude (length) of a vector
find the direction of a vector
add vectors
subtract vectors
multiply a vector by a scalar
express a vector in terms of the standard basis vectors i, j, and k
find the dot product of two vectors
use the dot product to solve application problems
find the cross product of two vectors
use the cross product to solve application problems
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Analyze equations in three-dimensional space
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
construct graphs of conic sections
interpret graphs of conic sections
plot points in the 3D rectangular coordinate system
sketch surfaces in the 3D rectangular coordinate system
find the distance between two points in 3D space by using the distance formula
find the equation of a sphere with a given center and radius
identify cylinders
use traces to identify quadric surfaces
find the equation of a line in 3D
find the equation a plane in 3D
solve application problems involving lines and planes in 3D
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Analyze plane curves using parametric equations
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
sketch the curve represented by parametric equations
describe the motion represented by parametric equations
construct parametric equations that represent a given curve and motion along it
use integrals in parametric form to solve application problems
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Analyze graphs using polar coordinates
Assessment Strategies
Quiz, Exam, Written Product, and/or Projects
Criteria
plot a point in polar coordinates
convert points between rectangular and polar coordinates
convert equations between rectangular and polar form
sketch the graph of a polar equation
use integrals in polar form to solve application problems