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Calculus I
The Latest Version A+ Study Guide
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MTH 280 Entire Course
https://uopcourses.com/category/mth-280/
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MTH 280 Week 1MyMathLab Study Plan for Weekly Checkpoint
1.1 Functions and Their Graphs
o Find the domain and range of functions.
o Determine if graphs represent functions.
o Graph and identify symmetries of a function and state where it is increasing and decreasing.
1.2 Combining Functions; Shifting and Scaling Graphs
o Identify and write equations for functions that involve translations.
o Shift the graph of a function and write an equation for the shifted graph.
o Graph functions using transformations.
o Identify and write equations for functions that involve scaling.
1.3 Trigonometric Functions
o Use the arc length formula.
o Evaluate trigonometric functions.
o Graph and identify characteristics of trigonometric functions.
o Use the addition formulas for sine and cosine.
o Use the half-angle formulas for sine and cosine.
o Solve trigonometric equations.
o Use the law of sines and the law of cosines.
2.1 Rates of Change and Tangents to Curves
o Find the average rate of change of a function over an interval.
o Find the slope of the tangent line at a given point.
2.2 Limit of a Function and Limit Laws
o Find the limit from graphs.
o Find the limit of algebraic functions.
o Find the limit of trigonometric functions.
o Find the limit using the rules for limits.
o Evaluate the limit of average rates of change.
o Use the Sandwich Theorem.
o Estimate limits.
MTH 280 Weekly MyMathLabWeek 1 Checkpoint
1.1 Functions and Their Graphs
o Find the domain and range of functions.
o Determine if graphs represent functions.
o Graph and identify symmetries of a function and state where it is increasing and decreasing.
1.2 Combining Functions; Shifting and Scaling Graphs
o Identify and write equations for functions that involve translations.
o Shift the graph of a function and write an equation for the shifted graph.
o Graph functions using transformations.
o Identify and write equations for functions that involve scaling.
1.3 Trigonometric Functions
o Use the arc length formula.
o Evaluate trigonometric functions.
o Graph and identify characteristics of trigonometric functions.
o Use the addition formulas for sine and cosine.
o Use the half-angle formulas for sine and cosine.
o Solve trigonometric equations.
o Use the law of sines and the law of cosines.
2.1 Rates of Change and Tangents to Curves
o Find the average rate of change of a function over an interval.
o Find the slope of the tangent line at a given point.
2.2 Limit of a Function and Limit Laws
o Find the limit from graphs.
o Find the limit of algebraic functions.
o Find the limit of trigonometric functions.
o Find the limit using the rules for limits.
o Evaluate the limit of average rates of change.
o Use the Sandwich Theorem.
o Estimate limits.
MTH 280 Week 2MyMathLab Study Plan for Weekly Checkpoint
2.3 The Precise Definition of a Limit
Find delta graphically.
Find delta algebraically.
Solve applications involving limits.
2.4 One-Sided Limits
Find one-sided limits graphically.
Find one-sided limits algebraically.
2.5 Continuity
Determine where functions are continuous.
Find limits involving trigonometric functions.
Find values that make a function continuous.
Use continuity and the intermediate value theorem to solve problems.
Analyze concepts involving continuous functions.
2.6 Limits Involving Infinity; Asymptotes of Graphs
Find limits using a graph of the function.
Find limits as x approaches infinity or negative infinity.
Find limits approaching a real number.
Graph rational functions.
Find and graph a function with the given conditions.
MTH 280 Weekly MyMathLabWeek 2 Checkpoint
2.3 The Precise Definition of a Limit
Find delta graphically.
Find delta algebraically.
Solve applications involving limits.
2.4 One-Sided Limits
Find one-sided limits graphically.
Find one-sided limits algebraically.
2.5 Continuity
Determine where functions are continuous.
Find limits involving trigonometric functions.
Find values that make a function continuous.
Use continuity and the intermediate value theorem to solve problems.
Analyze concepts involving continuous functions.
2.6 Limits Involving Infinity; Asymptotes of Graphs
Find limits using a graph of the function.
Find limits as x approaches infinity or negative infinity.
Find limits approaching a real number.
Graph rational functions.
Find and graph a function with the given conditions.
MTH 280 Week 3MyMathLab Study Plan for Weekly Checkpoint
3.1 Tangents and the Derivative at a Point
Find the slope of the tangent line at given points.
Find the equation of the tangent line at given points.
Solve applications involving tangent lines at a point.
Find points on a curve that have desired tangent lines.
Find vertical tangents of a curve.
3.2 The Derivative as a Function
Calculate the derivatives of functions.
Find the slope of the tangent line for a function at a given value.
Find the equation of the tangent line at a given point of a function.
Use the alternative formula for derivatives to find the derivative of a function.
Find the derivative of a graphed function.
Solve applications involving derivatives.
Determine if functions are differentiable at certain points.
3.3 Differentiation Rules
Find the first and second derivatives of a function.
Find the first derivative of a function.
Find the derivatives of all orders of a function.
Find slopes and tangents of a function.
Solve applications involving differentiation.
3.4 The Derivative as a Rate of Change
Solve applications involving rate of change.
Analyze motion using graphs.
3.5 Derivatives of Trigonometric Functions
Find derivatives of trigonometric functions.
Find and graph tangent lines for given values of trigonometric functions.
Evaluate limits involving trigonometric functions.
MTH 280 Weekly MyMathLabWeek 3 Checkpoint
3.1 Tangents and the Derivative at a Point
Find the slope of the tangent line at given points.
Find the equation of the tangent line at given points.
Solve applications involving tangent lines at a point.
Find points on a curve that have desired tangent lines.
Find vertical tangents of a curve.
3.2 The Derivative as a Function
Calculate the derivatives of functions.
Find the slope of the tangent line for a function at a given value.
Find the equation of the tangent line at a given point of a function.
Use the alternative formula for derivatives to find the derivative of a function.
Find the derivative of a graphed function.
Solve applications involving derivatives.
Determine if functions are differentiable at certain points.
3.3 Differentiation Rules
Find the first and second derivatives of a function.
Find the first derivative of a function.
Find the derivatives of all orders of a function.
Find slopes and tangents of a function.
Solve applications involving differentiation.
3.4 The Derivative as a Rate of Change
Solve applications involving rate of change.
Analyze motion using graphs.
3.5 Derivatives of Trigonometric Functions
Find derivatives of trigonometric functions.
Find and graph tangent lines for given values of trigonometric functions.
Evaluate limits involving trigonometric functions.
MTH 280 Week 4MyMathLab Study Plan for Weekly Checkpoint
3.6 The Chain Rule
Use the Chain Rule to find first derivatives.
Use the Chain Rule to find second derivatives.
Use the Chain Rule to evaluate derivatives at given values.
Solve theory problems involving the Chain Rule.
Solve applications involving the Chain Rule.
3.7 Implicit Differentiation
Use implicit differentiation to find first derivatives.
Use implicit differentiation to find second derivatives.
Work with slope, tangent lines, and normal lines.
Solve theory problems involving implicit differentiation.
Solve problems involving orthogonal curves.
3.8 Related Rates
Solve related rate equations.
Understand how rates of change relate.
Solve applications involving related rates.
3.9 Linearization and Differentials
Find the linearization of functions.
Use the approximation (1+x)^k=1+kx.
Find the change in f, the value of the estimate df, and the approximation error.
Find differential formulas that estimate changes in volume or surface area.
Solve applications involving linearization and differentials.
MTH 280 Weekly MyMathLabWeek 4 Checkpoint
3.6 The Chain Rule
Use the Chain Rule to find first derivatives.
Use the Chain Rule to find second derivatives.
Use the Chain Rule to evaluate derivatives at given values.
Solve theory problems involving the Chain Rule.
Solve applications involving the Chain Rule.
3.7 Implicit Differentiation
Use implicit differentiation to find first derivatives.
Use implicit differentiation to find second derivatives.
Work with slope, tangent lines, and normal lines.
Solve theory problems involving implicit differentiation.
Solve problems involving orthogonal curves.
3.8 Related Rates
Solve related rate equations.
Understand how rates of change relate.
Solve applications involving related rates.
3.9 Linearization and Differentials
Find the linearization of functions.
Use the approximation (1+x)^k=1+kx.
Find the change in f, the value of the estimate df, and the approximation error.
Find differential formulas that estimate changes in volume or surface area.
Solve applications involving linearization and differentials.
MTH 280 Week 5MyMathLab Study Plan for Weekly Checkpoint
4.1 Extreme Values of Functions
Find extreme values and where they occur.
Find absolute extrema on finite closed intervals.
Find all critical points for a function.
Find critical points and local extrema.
Solve applications involving extreme values of functions.
4.2 The Mean Value Theorem
Find the values that satisfy the conclusion of the mean value theorem.
Find the values of functions given the derivatives.
Find functions from given derivatives at a given point.
Solve applications involving the mean value theorem.
4.3 Monotonic Functions and the First Derivative Test
Given the derivative, find increasing and decreasing intervals and extrema.
Given the function, find increasing and decreasing intervals and extrema.
Find local and absolute extrema in a given domain.
4.4 Concavity and Curve Sketching
Identify the inflection points, local extrema, and concavity from graphs.
Graph functions, and find any local extrema and inflection points.
Sketch the general graph of functions given the equation of the derivatives.
Graph f(x) given the graphs of f’(x) and f’’(x).
Graph rational functions.
Graph functions given certain conditions.
Solve applications involving concavity and curve sketching.
MTH 280 Weekly MyMathLabWeek 5 Checkpoint
4.1 Extreme Values of Functions
Find extreme values and where they occur.
Find absolute extrema on finite closed intervals.
Find all critical points for a function.
Find critical points and local extrema.
Solve applications involving extreme values of functions.
4.2 The Mean Value Theorem
Find the values that satisfy the conclusion of the mean value theorem.
Find the values of functions given the derivatives.
Find functions from given derivatives at a given point.
Solve applications involving the mean value theorem.
4.3 Monotonic Functions and the First Derivative Test
Given the derivative, find increasing and decreasing intervals and extrema.
Given the function, find increasing and decreasing intervals and extrema.
Find local and absolute extrema in a given domain.
4.4 Concavity and Curve Sketching
Identify the inflection points, local extrema, and concavity from graphs.
Graph functions, and find any local extrema and inflection points.
Sketch the general graph of functions given the equation of the derivatives.
Graph f(x) given the graphs of f’(x) and f’’(x).
Graph rational functions.
Graph functions given certain conditions.
Solve applications involving concavity and curve sketching.
MTH 280 Week 6MyMathLab Study Plan for Weekly Checkpoint
4.5 Applied Optimization
Solve mathematical and geometric applications.
Solve physical applications.
Solve applications about business and economics.
Solve applications about biology.
Solve theory problems involving optimization.
4.6 Newton’s Method
Use Newton’s method to find solutions to equations.
Use Newton’s method to find zeros of functions.
Solve theory and applications involving Newton’s method.
4.7 Antiderivatives
Find antiderivatives or indefinite integrals.
Verify formulas using differentiation.
Solve initial value problems.
Solve applications involving antiderivatives.
MTH 280 Weekly MyMathLabWeek 6 Checkpoint
4.5 Applied Optimization
Solve mathematical and geometric applications.
Solve physical applications.
Solve applications about business and economics.
Solve applications about biology.
Solve theory problems involving optimization.
4.6 Newton’s Method
Use Newton’s method to find solutions to equations.
Use Newton’s method to find zeros of functions.
Solve theory and applications involving Newton’s method.
4.7 Antiderivatives
Find antiderivatives or indefinite integrals.
Verify formulas using differentiation.
Solve initial value problems.
Solve applications involving antiderivatives.
MTH 280 Week 7MyMathLab Study Plan for Final Examination
1.1 Functions and Their Graphs
o Find the domain and range of functions.
o Determine if graphs represent functions.
o Graph and identify symmetries of a function and state where it is increasing and decreasing.
1.2 Combining Functions; Shifting and Scaling Graphs
o Identify and write equations for functions that involve translations.
o Shift the graph of a function and write an equation for the shifted graph.
o Graph functions using transformations.
o Identify and write equations for functions that involve scaling.
1.3 Trigonometric Functions
o Use the arc length formula.
o Evaluate trigonometric functions.
o Graph and identify characteristics of trigonometric functions.
o Use the addition formulas for sine and cosine.
o Use the half-angle formulas for sine and cosine.
o Solve trigonometric equations.
o Use the law of sines and the law of cosines.
2.1 Rates of Change and Tangents to Curves
o Find the average rate of change of a function over an interval.
o Find the slope of the tangent line at a given point.
2.2 Limit of a Function and Limit Laws
o Find the limit from graphs.
o Find the limit of algebraic functions.
o Find the limit of trigonometric functions.
o Find the limit using the rules for limits.
o Evaluate the limit of average rates of change.
o Use the Sandwich Theorem.
o Estimate limits.
2.3 The Precise Definition of a Limit
Find delta algebraically.
Solve applications involving limits.
2.4 One-Sided Limits
Find one-sided limits graphically.
Find one-sided limits algebraically.
2.5 Continuity
Determine where functions are continuous.
Find limits involving trigonometric functions.
Use continuity and the intermediate value theorem to solve problems.
2.6 Limits Involving Infinity; Asymptotes of Graphs
Find limits as x approaches infinity or negative infinity.
Find limits approaching a real number.
Graph rational functions.
3.1 Tangents and the Derivative at a Point
Find the equation of the tangent line at given points.
Solve applications involving tangent lines at a point.
3.2 The Derivative as a Function
Calculate the derivatives of functions.
Find the derivative of a graphed function.
Determine if functions are differentiable at certain points.
3.3 Differentiation Rules
Find the first and second derivatives of a function.
Find slopes and tangents of a function.
Solve applications involving differentiation.
3.4 The Derivative as a Rate of Change
Solve applications involving rate of change.
Analyze motion using graphs.
3.5 Derivatives of Trigonometric Functions
Find derivatives of trigonometric functions.
Find and graph tangent lines for given values of trigonometric functions.
3.6 The Chain Rule
Use the Chain Rule to find first derivatives.
Use the Chain Rule to evaluate derivatives at given values.
3.7 Implicit Differentiation
Use implicit differentiation to find second derivatives.
3.8 Related Rates
Understand how rates of change relate.
Solve applications involving related rates.
3.9 Linearization and Differentials
Find the linearization of functions.
Use the approximation (1+x)^k=1+kx.
Solve applications involving linearization and differentials.
4.1 Extreme Values of Functions
Find extreme values and where they occur.
Find absolute extrema on finite closed intervals.
Find all critical points for a function.
Solve applications involving extreme values of functions.
4.2 The Mean Value Theorem
Find the values of functions given the derivatives.
4.3 Monotonic Functions and the First Derivative Test
Given the function, find increasing and decreasing intervals and extrema.
4.4 Concavity and Curve Sketching
Sketch the general graph of functions given the equation of the derivatives.
Solve applications involving concavity and curve sketching.
4.5 Applied Optimization
Solve mathematical and geometric applications.
Solve applications about business and economics.
4.6 Newton’s Method
Use Newton’s method to find solutions to equations.
4.7 Antiderivatives
Find antiderivatives or indefinite integrals.
MTH 280 Weekly MyMathLabWeek 7 Final Examination
1.1 Functions and Their Graphs
o Find the domain and range of functions.
o Determine if graphs represent functions.
o Graph and identify symmetries of a function and state where it is increasing and decreasing.
1.2 Combining Functions; Shifting and Scaling Graphs
o Identify and write equations for functions that involve translations.
o Shift the graph of a function and write an equation for the shifted graph.
o Graph functions using transformations.
o Identify and write equations for functions that involve scaling.
1.3 Trigonometric Functions
o Use the arc length formula.
o Evaluate trigonometric functions.
o Graph and identify characteristics of trigonometric functions.
o Use the addition formulas for sine and cosine.
o Use the half-angle formulas for sine and cosine.
o Solve trigonometric equations.
o Use the law of sines and the law of cosines.
2.1 Rates of Change and Tangents to Curves
o Find the average rate of change of a function over an interval.
o Find the slope of the tangent line at a given point.
2.2 Limit of a Function and Limit Laws
o Find the limit from graphs.
o Find the limit of algebraic functions.
o Find the limit of trigonometric functions.
o Find the limit using the rules for limits.
o Evaluate the limit of average rates of change.
o Use the Sandwich Theorem.
o Estimate limits.
2.3 The Precise Definition of a Limit
Find delta algebraically.
Solve applications involving limits.
2.4 One-Sided Limits
Find one-sided limits graphically.
Find one-sided limits algebraically.
2.5 Continuity
Determine where functions are continuous.
Find limits involving trigonometric functions.
Use continuity and the intermediate value theorem to solve problems.
2.6 Limits Involving Infinity; Asymptotes of Graphs
Find limits as x approaches infinity or negative infinity.
Find limits approaching a real number.
Graph rational functions.
3.1 Tangents and the Derivative at a Point
Find the equation of the tangent line at given points.
Solve applications involving tangent lines at a point.
3.2 The Derivative as a Function
Calculate the derivatives of functions.
Find the derivative of a graphed function.
Determine if functions are differentiable at certain points.
3.3 Differentiation Rules
Find the first and second derivatives of a function.
Find slopes and tangents of a function.
Solve applications involving differentiation.
3.4 The Derivative as a Rate of Change
Solve applications involving rate of change.
Analyze motion using graphs.
3.5 Derivatives of Trigonometric Functions
Find derivatives of trigonometric functions.
Find and graph tangent lines for given values of trigonometric functions.
3.6 The Chain Rule
Use the Chain Rule to find first derivatives.
Use the Chain Rule to evaluate derivatives at given values.
3.7 Implicit Differentiation
Use implicit differentiation to find second derivatives.
3.8 Related Rates
Understand how rates of change relate.
Solve applications involving related rates.
3.9 Linearization and Differentials
Find the linearization of functions.
Use the approximation (1+x)^k=1+kx.
Solve applications involving linearization and differentials.
4.1 Extreme Values of Functions
Find extreme values and where they occur.
Find absolute extrema on finite closed intervals.
Find all critical points for a function.
Solve applications involving extreme values of functions.
4.2 The Mean Value Theorem
Find the values of functions given the derivatives.
4.3 Monotonic Functions and the First Derivative Test
Given the function, find increasing and decreasing intervals and extrema.
4.4 Concavity and Curve Sketching
Sketch the general graph of functions given the equation of the derivatives.
Solve applications involving concavity and curve sketching.
4.5 Applied Optimization
Solve mathematical and geometric applications.
Solve applications about business and economics.
4.6 Newton’s Method
Use Newton’s method to find solutions to equations.
4.7 Antiderivatives
Find antiderivatives or indefinite integrals.
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