Calculus Flashcards
1
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2.1 Definition of the Derivative of a Function
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2
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2.2: The Constant Rule
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3
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2.2: The Power Rule
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4
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2.2: The Constant Multiple Rule
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5
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2.2: The Sum and Difference Rules
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6
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2.2: Derivative of Sine Function
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7
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2.2: Derivative of Cosine Function
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8
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2.3: The Product Rule
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2.3: The Quotient Rule
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10
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2.3: Derivative of Tangent Function
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11
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2.3: Derivative of Cosecant Function
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12
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2.3: Derivative of Secant Function
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13
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2.3: Derivative of Cotangent Function
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14
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2.4: The Chain Rule
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15
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2.4: The General Power Rule
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16
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2.5: Guidelines for Implicit Differentiation
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17
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2.6: Guidelines for Rate-Related Problem
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18
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3.1: The Extreme Value Theorem
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19
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3.1: Guidelines for Finding Extrema on a Closed Interval
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20
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3.2: Rolle’s Theorem
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21
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3.2: The Mean Value Theorem
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22
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3.3: The First Derivative Test
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23
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3.3: The Derivative and Increasing and Decreasing Functions
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24
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3.4: Test for Concavity
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3.4: Points of Inflection
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3.4: The Second Derivative Test
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3.7: Guidlines for Solving Applied Minimum and Maximum Problems
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3.8: Newton's Method for Approximating the Zeros of a Function
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3.9: Tangent Line approximation of *f* at *c*
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3.9: Differential of *y*
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4.1: The Constant Rule of Integration
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4.1:
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4.1: The Constant Multiple Rule of Integration
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4.1: The Sum and Difference Rules of Integration
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4.1: The Power Rule of Integration
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4.1: Integral of Cosine Function
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4.1: Integral of Sine Function
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4.1: Integral of Secant Squared Function
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4.1: Integral of Secant Tangent Function
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4.1: Integral of Cosecant Squared Function
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4.1: Integral of Cosecant Cotangent Function
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4.2: Summation Formulas
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4.2: Finding Upper and Lower Sums for a Region
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4.2: Definition of the Area of a Region in the Plane
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4.4: Mean Value Theorem for Integrals
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4.4: Average Value of a Function
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4.4: The Second Fundamental Theorem of Calculus
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4.4: The Net Change Theorem
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4.5: The General Power Rule for Integrals
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4.5: Change of Variables for Definite Integration
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4.5: Change of Variables Integration
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4.6: The Trapezoidal Rule
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4.6: Errors in the Trapezoidal Rule
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4.6: Simpon's Rule
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4.6: Error in Simpson's Rule
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5.1: Logarithmic Properties
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5.1: The Derivative of Logarithmic Functions
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5.2: Log Rule for Integration
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5.2: Integral of the Tangent Function
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5.2: Integral of the Secant Function
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5.2: Integral of the Cosecant Function
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5.2: Integral of the Cotangent Function
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5.4: Derivative of Exponential Functions
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5.4: Integral of Exponential Functions
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5.6: Derivatives of Inverse Trigonometric Functions
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5.7: Integrals Involving Inverse Trigonometric Functions
Let *u* be a differentiable function of *x*, and let *a* \>0.
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5.8: Definitions of Hyperbolic Functions
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5.8: Derivatives of Hyperbolic Functions
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5.8: Derivatives of Inverse Hyperbolic Functions
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7.1: Area of a Region Between Two Curves
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7.1: Area of a Region Between Two Intersecting Curves
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7.2: The Disk Method of a Solid of Revolution
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7.2: The Washer Method of a Solid of Revolution
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7.2: Volume of Solids with Known Cross Section
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7.3: The Shell Method of a Solid of Revolution
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7.4: Length of a Curve
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7.4: Area of a Surface of Revolution
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7.5: Work Done by a Variable Force
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7.5: Hooke's Law Equation
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7.5: Newton's Law of Universal Gravitation
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7.5: Coulomb's Law Equation
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7.6: Moments and Center of Mass of a Planar Lamina
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7.6: The Theorem of Pappus Equation
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7.7: Definition of Fluid Pressure
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7.7: Force Exerted by a Fluid
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8.2: Integration by Parts
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9.2: Geometric Series
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9.3: The Integral Test
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9.3: p-series
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9.3: Harmonic Series
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9.4: Direct Comparison Test for Convergen and Divergence
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9.4: Limit Comparison Test
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9.5: Alternating Series Test
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9.5: Absolute and Conditional Convergence
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9.6: The Ratio Test
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9.6: The Root Test
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9.7: Taylor Polyomial
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9.7: Maclaurin Polynomial
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8.5 Partial Fraction Decomposition
Example:
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9.2: Nth-term Test for Divergence
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9.5: Alternating Series Remainder
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9.8 Power Series
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9.8: Finding the Interval of Convergence for Power Series
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9.10: Taylor Series and Maclaurin Series
