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

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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Derivatives and Applications: MATH 171 Problems 7 & 8 thumbnail

Derivatives and Applications: MATH 171 Problems 7 & 8

Calculating slopes of tangent lines to parametric curves

CosineDerivativeLimitLimit from the LeftLimit from the RightLimit Involving InfinityParametric EquationsPerpendicularPolynomialProduct RuleSineTangent LineVectorVector Derivative
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Limits: MATH 171 Problem 7 thumbnail

Limits: MATH 171 Problem 7

Proving a property for limits of sums using the epsilon-delta definition

Absolute ValueEpsilon-Delta Definition of a LimitLimitLimit Properties
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Limits: MATH 171 Problems 8 & 9 thumbnail

Limits: MATH 171 Problems 8 & 9

Proving a property of scalar multiplication for limits using the epsilon-delta definition and using the Squeeze Theorem for Limits.

Absolute ValueCosineEpsilon-Delta Definition of a LimitLimitLimit PropertiesScalarSquare RootSqueeze (or Sandwich) TheoremTrigonometry
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Precise Definition of a Limit: MATH 171 Problems 3 & 4 thumbnail

Precise Definition of a Limit: MATH 171 Problems 3 & 4

Proving limits using the epsilon-delta definition

Absolute ValueEpsilon-Delta Definition of a LimitLimitLine
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Precise Definition of a Limit: MATH 171 Problems 5 & 6 thumbnail

Precise Definition of a Limit: MATH 171 Problems 5 & 6

Proving limits using the epsilon-delta definition

Absolute ValueEpsilon-Delta Definition of a LimitInfinite LimitLimitLimit from the Right
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Continuity: MATH 171 Problems 6 & 7 thumbnail

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 thumbnail

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 thumbnail

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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