OC user

in MathematicsÂ·

17 Sep 2020

- Calculus 1
- Apply Rolle's Theorem
- Find the derivatives of inverse trigonometric functions
- Use logarithmic differentiation
- Solve optimization problems
- Apply first and second derivative tests
- Find extreme values and critical points
- Apply implicit differentiation and solve for related rates
- Find the definition of the derivative
- Calculate limits
- Find tangent line equations
- Evaluate logarithmic functions
- Evaluate exponential functions
- Evaluate trigonometric functions
- Combine functions
- Transform functions
- Set up and solve function word problems
- Sketch functions
- Determine properties of functions

- General Chemistry 1
- Solve problems relating to the Born-Haber Cycle
- Solve problems relating to Coulomb's Law and properties of ionic compounds
- Solve problems relating to vapor pressure and phase diagrams
- Assess problems relating to intermolecular forces
- Apply the Molecular Orbital Theory
- Apply Lewis, VSEPR, and Valence Bond Theory simultaneously
- Assess dipole moment, polarity, bond order, bond length, and bond energies
- Apply the VSEPR Theory
- Assess electronegativity differences and polarity of bonds
- Draw Lewis structures with exceptions to the octet rule
- Draw Lewis structures
- Solve problems relating to the periodic table and its trends
- Solve problems relating to electron configuration
- Solve problems relating to quantum numbers
- Solve problems relating to quantum mechanics
- Solve problems relating to atomic spectra of hydrogen
- Solve problems relating to electromagnetic radiation
- Solve problems relating to Hess's Law and standard enthalpies of formation
- Solve problems relating to enthalpy and internal energy
- Solve problems relating to pressure-volume work
- Solve problems relating to calorimetry
- Solve problems relating to quantity of heat
- Solve problems relating to real gases
- Solve problems relating to Graham's Law
- Solve problems relating to kinetic-molecular theory
- Solve problems relating to collecting a gas over water
- Solve problems relating to Dalton's Law of Partial Pressures
- Solve problems relating to the ideal gas law
- Solve problems relating to simple gas laws
- Use a manometer to measure gas pressure
- Write redox equations
- Write net ionic equations
- Solve problems relating to limiting reactant
- Solve problems relating to stoichiometry
- Name compounds
- Assign oxidation states
- Solve problems relating to empirical and molecular formulas
- Solve problems relating to Avogadro's number, moles, and mass
- Solve problems relating to isotopes
- Identify the number of protons, neutrons, and electrons in atoms and ions
- Apply laws to solve problems
- Classify matter
- Report measurement

- Calculus 2
- Solve problems relating to Taylor and Maclaurin series
- Solve problems relating to power series
- Solve problems relating to convergence and divergence
- Solve problems relating to the Alternating Series Estimation Theorem
- Solve problems relating to conditional convergence
- Solve problems relating to absolute convergence
- Solve problems relating to comparison tests
- Solve problems relating to the P-Series Test
- Solve problems relating to the Integral Test
- Solve problems relating to the Nth Term Test
- Find the telescopic sum
- Solve problems relating to geometric series
- Solve problems relating to partial sums
- Solve problems relating to sequences
- Evaluate improper integrals by cases
- Apply integration techniques
- Use integration to find the work done
- Find the volume of a solid of revolution
- Solve problems relating to arc length
- Use numerical integration
- Solve problems relating to intersection of polar curves
- Solve problems relating to logistic models
- Analyze phase planes
- Solve problems relating to parametric curves
- Find the area under the curve
- Solve problems relating to first-order differential equations
- Apply Euler's method
- Solve problems relating to polar coordinates
- Sketch slope fields
- Solve problems relating to polar coordinate equations
- Solve problems relating to area in polar coordinates

- AP Calculus AB
- Integrate using substitution
- Find the area between curves expressed as functions of y
- Find particular solutions using initial conditions and separation of variables
- Use the first and second derivative test to determine relative (local) extrema
- Determine limits by the Squeeze Theorem
- Define continuity at a point
- Confirm continuity over an interval
- Connect infinite limits and vertical asymptotes
- Connect limits at infinity and horizontal asymptotes
- Work with the Intermediate Value Theorem
- Apply derivative rules: power, constant, sum, difference, and constant multiple
- Apply the Chain Rule
- Sketch graphs of functions and their derivatives
- Solve Riemann sums, summation notation, and definite integral notation
- Estimate limit values from graphs and tables
- Define the derivative of a function and use derivative notations
- Solve volume with disc method: revolving around the x- or y-axis
- Connect differentiability and continuity: determine when derivatives do and do not exist
- Solve derivatives of trigonometric and natural logarithmic functions
- Determine limits by limit properties
- Determine limits by direct substitution
- Determine limits by algebraic manipulation
- Connect multiple representations of limits
- Define average and instantaneous rates of change at a point
- Apply the Product Rule and Quotient Rule
- Use implicit differentiation
- Differentiate inverse functions
- Calculate higher-order derivatives
- Interpret the meaning of the derivative in context
- Straight-line motion: connect position, velocity, and acceleration
- Approximate values of a function using local linearity and linearization
- Solve problems relating to Extreme Value Theorem, global vs. local extrema, and critical points
- Determine intervals on which a function is increasing or decreasing
- Use the candidates test to determine absolute (global) extrema
- Determine concavity of functions over their domains
- Approximate areas with Riemann sums
- Solve the fundamental theorem of calculus and accumulation functions
- Interpret the behavior of accumulation functions involving area
- Apply properties of definite integrals
- Find antiderivatives and indefinite integrals: basic rules and notation
- Find antiderivatives and definite integrals: basic rules and notation - Part 1
- Find antiderivatives and definite integrals: basic rules and notation - Part 2
- Integrate functions using long division and complete the square
- Select techniques for antidifferentiation
- Find the average value of a function on an interval
- Connect position, velocity, and acceleration of functions using integrals
- Use accumulation functions and definite integrals in applied contexts
- Find the area between curves expressed as functions of x
- Find the area between curves that intersect at more than two points
- Solve volumes with cross sections: squares and rectangles
- Solve volumes with cross sections: triangles and semicircles
- Solve volume with disc method: revolving around other axes
- Solve volume with washer method: revolve around the x- or y-axis
- Solve volume with washer method: revolve around other axes
- Model situations with differential equations
- Verify solutions for differential equations
- Sketch slope fields
- Reason using slope fields
- Find general solutions using separation of variables
- Solve exponential models with differential equations

- AP Calculus BC
- Work with the Intermediate Value Theorem
- [BC only] Evaluate improper integrals
- Find the derivatives of tan, cot, sec, and/or csc functions
- Use implicit differentiation
- Straight-line motion: connect position, velocity, and acceleration
- Find the area between curves expressed as functions of y
- Solve volumes with cross sections: squares and rectangles
- Solve volume with disc method: revolving around other axes
- Solve volume with washer method: revolve around other axes
- [BC only] Solve the arc length of a smooth, planar curve and distance traveled
- Model situations with differential equations
- Sketch slope fields
- Find radius and interval of convergence of power series
- Determine intervals on which a function is increasing or decreasing
- Use the first and second derivative test to determine relative (local) extrema
- Determine concavity of functions over their domains
- Interpret the behavior of accumulation functions involving area
- Connect position, velocity, and acceleration of functions using integrals
- Apply the Chain Rule
- Differentiate inverse functions
- Interpret the meaning of the derivative in context
- Approximate values of a function using local linearity and linearization
- Find antiderivatives and indefinite integrals: basic rules and notation
- Integrate using substitution
- Find the area between curves that intersect at more than two points
- Apply derivative rules: power, constant, sum, difference, and constant multiple
- Find the area of the region bounded by two polar curves
- Apply the Comparison Tests for convergence
- Determine limits by the Squeeze Theorem
- Determine limits by algebraic manipulation
- Determine limits by direct substitution
- Estimate limit values from graphs and tables
- Determine limits by limit properties
- Confirm continuity over an interval
- Connect infinite limits and vertical asymptotes
- Connect limits at infinity and horizontal asymptotes
- Connect multiple representations of limits
- Define continuity at a point
- Define average and instantaneous rates of change at a point
- Define the derivative of a function and use derivative notations
- Connect differentiability and continuity: determine when derivatives do and do not exist
- Apply the Product Rule and Quotient Rule
- Solve derivatives of cos x, sin x, e^x, and ln x
- Calculate higher-order derivatives
- Use the candidates test to determine absolute (global) extrema
- Solve problems relating to Extreme Value Theorem, global vs. local extrema, and critical points
- Approximate areas with Riemann sums
- Sketch graphs of functions and their derivatives
- Solve Riemann sums, summation notation, and definite integral notation
- Apply properties of definite integrals
- Find antiderivatives and definite integrals: basic rules and notation - Part 1
- Find antiderivatives and definite integrals: basic rules and notation - Part 2
- Solve the fundamental theorem of calculus and accumulation functions
- Find the area between curves expressed as functions of x
- Use accumulation functions and definite integrals in applied contexts
- Select techniques for antidifferentiation
- Find the average value of a function on an interval
- Integrate functions using long division and complete the square
- [BC only] Integrate using integration by parts
- Solve volumes with cross sections: triangles and semicircles
- Solve volume with disc method: revolving around the x- or y-axis
- Solve volume with washer method: revolve around the x- or y-axis
- Verify solutions for differential equations
- Reason using slope fields
- [BC only] Approximate solutions using Euler's method
- Find general solutions using separation of variables
- Find particular solutions using initial conditions and separation of variables
- Solve exponential models with differential equations
- [BC only] Solve logistic models with differential equations
- Define and differentiate parametric equations
- Integrate vector-valued functions
- Find arc lengths of curves given by parametric equations
- Define polar coordinates and differentiate in polar form
- Solve motion problems using parametric and vector-valued functions
- Find the area of a polar region or area bounded by a single polar curve
- Find second derivatives of parametric equations
- Define and differentiate vector-valued functions
- Apply the Harmonic Series and P-Series
- Define convergent and divergent infinite series
- Apply the Integral Test for convergence
- Work with geometric series
- Apply the Ratio Test for convergence
- Apply the Nth Term Test for divergence
- Apply the Alternating Series Test for convergence
- Represent functions as power series
- Apply alternating series error bound
- Apply Lagrange error bound
- Determine absolute or conditional convergence
- Find Taylor or Maclaurin series for a function
- Find Taylor polynomial approximations of functions

- General Chemistry 2
- Solve problems relating to solubility and Ksp
- Solve problems relating to the equilibrium constant expression
- Relate equilibrium concentrations of reactants and products
- Solve problems relating to the effect of temperature on reaction rates
- Solve problems relating to the rate law
- Solve problems involving equilibrium calculations
- Solve problems involving Ecell as a function of concentrations
- Solve problems involving strong acids, strong bases, weak acids, and weak bases
- Solve problems involving acids, bases, and conjugate acid-base pairs
- Solve problems relating to standard Gibbs energy and K
- Solve problems involving redox reactions
- Use Le Chatelier's Principle, Q, and K
- Use molecular structure to predict acid-base behavior and demonstrate the common-ion effect
- Solve problems involving titrations
- Solve problems relating to entropy
- Measure reaction rates
- Solve problems relating to reaction mechanisms
- Solve problems relating to precipitation
- Solve problems involving electrolysis
- Solve problems relating to standard Gibbs energy
- Solve problems relating to reactions of various orders
- Solve problems involving buffer solutions
- Write equilibrium constant expressions for reactions involving pure solids or liquids
- Solve problems relating to polyprotic acids and ions as acids and bases
- Solve problems relating to zero-, first-, and second-order reactions

- AP Chemistry
- Solve problems involving galvanic (voltaic) and electrolytic cells
- Solve problems involving solubility equilibria
- Solve problems involving buffers and titrations
- Solve problems involving second-order reactions
- Solve problems involving nomenclature (molecular compounds)
- Solve problems involving ionic and net ionic equations
- Solve problems involving single- and double-replacement reactions
- Solve problems involving entropy and Gibbs free energy
- Solve problems involving spectroscopy and the electromagnetic spectrum
- Solve problems involving acid-base equilibria
- Solve problems involving atomic structure and electron configuration
- Solve problems involving gases
- Solve problems relating to Lewis structures and molecular geometry
- Solve problems involving compounds and ions
- Solve problems involving types of bonds
- Solve problems involving internal energy, heat, and work
- Solve problems involving nomenclature (ionic compounds)
- Solve problems involving zero- and first-order reactions
- Solve problems involving intermolecular forces
- Solve problems involving cell potentials under nonstandard conditions
- Solve problems involving the factors that affect chemical equilibrium
- Solve problems involving acids, bases, and pH
- Solve problems involving standard cell potentials
- Solve problems involving Arrhenius equation and reaction mechanisms
- Solve problems involving atoms
- Solve problems involving the equilibrium constant
- Solve problems involving reaction rates and the rate law
- Solve problems involving enthalpy
- Solve problems involving precipitation reactions
- Solve problems electrolytic cells and electrolysis
- Solve problems involving periodic table trends
- Solve problems involving solutions and mixtures
- Solve problems involving redox reactions

- Microeconomics
- Explain the functioning of a Monopoly, Anti-competitive behaviour and regulations
- Explaining the Theories of International Trade
- Understanding Insurance and Imperfect Information
- Explain and Analyze Efficiency in Perfect Competitive Markets
- Explaining the concept of Labor union
- Understanding How Businesses Raise Financial Capital
- Defining Negative Externality
- Identifying Government encouragement to innovation
- Explain key concepts in the process of Production in Short Run with key definitions
- Define and Calculate Different Types of Elasticity
- Finding out Market-Oriented Environmental Tools
- Defining Positive externality
- Explain the functioning of a Monopoly
- Elucidate definitions calculation and graphs of Costs and profit in short run
- Understanding Immigration
- Explaining Imperfect Information
- Understanding economic systems and globalization
- Understanding the concept of Public Goods
- Understanding International Externalities
- Explaining the Democratic System of Government
- Understanding Special Interest Politics
- Explain functioning of Monopolistic Competition and Oligopoly
- Identify and Explain Factors affecting Demand and Supply
- Understanding Ecotourism
- Elucidate Application of Demand and Supply
- Analyze Problems of Scarcity and Social Choices
- Define and Graph Demand, Supply and Equilibrium
- Explain Relationship between Consumer Choices and Utility
- Define and Explain Types of Costs and Profit
- Analyze Costs in the Long run
- Undertaking Marginal Analysis of pollution reduction
- Decoding Employment Discrimination
- Understanding Poverty
- Explaining Households Supply of Financial Capital
- Knowing about Public Economy
- Understanding the reason behind Intra-industry Trade between Similar Economies
- Understanding Protectionism
- Discusssing the Arguments in Support of Restricting Imports
- Explain the broad aspects of economic systems
- Explain Changes in Elasticity
- Analyze the Factors affecting Consumption Choices
- Explaining Income Inequality
- Finding out the Tradeoff between Economic Output and Environment
- Define and Analyze the Problems of Scarcity and Choices
- Evaluating the Government Policies to Reduce Income Inequality
- Define and Explain Perfect Competition - Price, Output and profit
- Explain and Analyze Price Controls, Surplus and Efficiency
- Understanding the Labor Markets

- Macroeconomics
- Graphs, variables, and economic models
- International Trade and Capital flows
- National debt
- Automatic stablizers
- Exchange rates demand and supply shifts
- Money Supply
- Aggregate Demand
- Unemployment and related terms
- Consumer Price Index
- GDP
- Basic Demand-Supply
- IS-LM Model
- Aggregate Supply
- Types of unemployment
- Computation of unemployment rate
- Understanding Inflation
- Causes of inflation
- Indexing
- Government spending
- Taxation
- Types of fiscal policy
- Discretionary fiscal policy
- Interest rates
- Federal Reserve System
- Money
- Inflation
- Velocity and Quantity equation
- Macro economics of open economies
- Foreign Exchange
- Exchange Rate polcies
- Loanable funds
- Policies and events affecting an open economy
- Globalization and Protectionism
- AD-AS Model Equilibrium
- Unemployment: Long run
- Discretionary fiscal policy
- Cost and Benefit of Inflation
- Monetary and Fiscal Policy: Application
- Unemployment: Short run
- Solving for Scarcity
- Measures of Inflation
- Opportunity Cost
- Phillips Curve
- Fiscal policy
- National Income
- Equilibrium and Stabilization

- Mechanics 1
- Understanding the aspects of acceleration due to gravity
- Understanding the concept of linear momentum
- Understanding the concept of angular motion
- Understanding the concept of center of mass and using them to solve problems
- Understanding the concept of energy
- Understanding the concept of collisions
- Understanding the concept of conservation of momentum
- Understanding phenomena based on gravity occurring in everyday life
- Graphing and using energy diagrams
- Applying the law of energy conservation
- Understanding potential energy
- Understanding work done by a variable force
- Understanding how work and kinetic energy are related
- Understanding the concept of power
- Understanding the concept of work
- Understanding the concepts of energy and kinetic energy
- Solving problems based on gravity
- Understanding the basics of motion and acceleration
- Understanding the basics of gravity
- Understanding frictional forces
- Understanding projectile motion
- Solving problems using Newton's Laws of Motion
- Understanding kinematic graphs
- Solving problems based on the equations of motion
- Understanding the concept of rotational motion

- Electricity and Magnetism
- Electric charge and application of Coulombâ€™s law
- Electric field and force on charges
- Electric potential and electric potential energy
- Understanding Series-Parallel circuit
- Understanding Gaussâ€™s law
- Understanding capacitors
- Understanding magnetic properties of matter
- Applying Gaussâ€™s law
- Understanding the combinations of capacitors and the energy stored in a capacitor
- Understanding DC Series circuit
- Understanding Krichoff's Law
- Understanding AC waveform
- Understanding inductive reactance
- Understanding capacitive reactance
- Understanding RLC circuit
- Understanding Power and Power Factor in an AC Circuit
- Understanding the production of induced EMF
- Solving problems by applying the concept of induced EMF
- Solving problems based on inductance
- Understanding energy stored in an inductor
- Solving problems based on the applications of electromagnetic induction
- Understanding dynamic or motional electromagnetic induction
- Understanding DC Parallel circuit
- Understanding Ohm's Law & Current electricity
- Understanding magnetic dipole moment
- Understanding the magnetic effect of an electric current
- Understanding the force on a moving charge in a magnetic field

Mathematics skill

- Integrate using long division
- Integrate using complete the square
- Integrate using the derivative of arctan(x)

Integrate functions using long division and complete the square Questions

Questions that need this skill to solve them

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

OC user

in MathematicsÂ·

17 Sep 2020

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