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Vector Functions: MATH 171 Problems 1 & 2

Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel

ParallelParameterizationParametric EquationsRational FunctionUnit CircleVectorVector Function

Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3

Proving facts about the derivatives of vector functions including the product rule

CosineDerivativeDifference QuotientDot ProductGraphLimitLimit Definition of the DerivativeOrthogonalProduct RuleSineSum RuleTrigonometryVectorVector DerivativeVector Function

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Inverse Trigonometric Functions: MATH 171 Problems 4-6

Properties of inverse trig functions and the derivative of arctangent

AngleArccosineArcsineArctangentCodomainCosineDerivativeDifferentiationDomainGraphInverse FunctionInverse TrigonometryOne-to-oneSecantSineTangentTrigonometry

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Continuity: MATH 171 Problems 6 & 7

Proving a piecewise function and a polynomial are continuous

ContinuousContinuous at x=aDiscontinuityDiscontinuous FunctionGraphLimitLimit PropertiesPiecewise FunctionPolynomialRational Function

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Continuity: MATH 171 Problems 8 & 9

Proving a product of continuous functions is continuous and using the Intermediate Value Theorem

ContinuousContinuous at x=aContinuous FunctionIntermediate Value TheoremLimitLimit PropertiesPolynomial

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Limits and Asymptotes: MATH 171 Problem 5

Proving a property for the limit of the difference of functions as x approaches infinity

Epsilon-Delta Definition of a LimitLimitLimit Involving InfinityLimit Properties

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Derivatives and Rates of Change: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

DerivativeDifference QuotientGraphLimitLimit Definition of the DerivativeLineRational FunctionSlopeSquare RootTangent LineVectorVector DerivativeVector Function

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