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Vector Functions: MATH 171 Problems 1 & 2 thumbnail

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

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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Differentials: MATH 171 Problems 1 & 2 thumbnail

Differentials: MATH 171 Problems 1 & 2

Proving facts about differentials including a product rule

DerivativeDifferentialLineLinear ApproximationProduct RuleTangent Line
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Exponentials and Hyperbolic Trigonometric Functions: MATH 171 Problems 3 & 4 thumbnail

Exponentials and Hyperbolic Trigonometric Functions: MATH 171 Problems 3 & 4

Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine

Chain RuleCosineDerivativeExponential FunctionHyperbolic CosineHyperbolic FunctionsHyperbolic SineHyperbolic TrigonometryLineSineTangent Linex-Intercept
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Studying the Shape of Curves: MATH 171 Problems 1-3 thumbnail

Studying the Shape of Curves: MATH 171 Problems 1-3

What the derivatives of a function tell us about the shape of its graph

Concave DownConcave UpDecreasingDecreasing FunctionDerivativeDiscontinuous FunctionFirst DerivativeGraphGraph of DerivativeIncreasingIncreasing FunctionLineRelative MaximumRelative MinimumSecond Derivative
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Optimization: MATH 171 Problems 1-3 thumbnail

Optimization: MATH 171 Problems 1-3

Optimizing values in word problems

Absolute MaximumAbsolute MinimumAreaCritical ValueDerivativeDistance from a Point to a LineFirst Derivative TestGraphIncreasing FunctionLineMaximizeMinimizeRelative MaximumRelative MinimumSecond Derivative TestVolumeWord Problems
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Definition of a Double-Log Plot thumbnail

Definition of a Double-Log Plot

Explaining the definition of logarithmic scale and double-log plots

Double-Log PlotGraphLineLogarithmLogarithmic ScaleMATH 147Power FunctionSlope
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