MTH 280 Weekly MyMathLab Week 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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