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