## Section Navigation

# MAT-281 Objectives

## MAT-281 Calculus I

### Chapter P

- Use absolute value to define an interval.
- Plot data on a cartesian graph.
- Use regression capabilities of a graphing calculator.
- Find intercepts.
- Sketch graphs of equations (absolute value, linear).
- Find points of intersection.
- Find slope and y-intercept.
- Write the equation of a line using.
- Two points
- One point and the slope.
- Write equations of lines parallel to a given line.
- Write equations of lines perpendicular to a given line.
- Evaluate a function at a given value.
- Identify y as a function of x.
- Find composite functions.
- Find Real zeros of a function.
- Write functions from word problems.
- Solve a quadratic equation.
- Simplify algebraic expressions.

### Chapter 1

- Use the definition of a limit to verify the validity of a limit. (Extra Credit!)
- Find the limit of an algebraic function.
- Find the limit of a trigonometric function.
- Find the limit of functions that begin as indeterminate.
- Find the limit of special trigonometric functions.
- Use the limit definition of velocity to solve falling object problems.
- Find one-sided limits of functions.
- Determine points of discontinuity.
- Identify discontinuities as removable or non-removable.
- Use interval notation to identify the domain of a function.
- Apply the Intermediate Value Theorem to the verification of a guaranteed value.
- Find vertical asymptotes of functions.
- Find one-sided infinite limits of functions.
- Apply limits to the solving of word problems.

### Chapter 2

- Use the definition of the derivative to find f'(x) .
- Find the equation of a tangent line to a graph of f at a point.
- Find the equation of a line tangent to f and parallel to a given line.
- Use the
*Alternative Form*of the derivative to find f'(c) . - Find values of x where f(x) is differentiable.
- Find the derivative of a given function.
- Evaluate the derivative of a function.
- Find the equation of a tangent line.
- Find the average rate of change.
- Solve falling body problems.
- Solve rate of change word problems.
- Differentiate algebraic functions.
- Differentiate trigonometric functions.
- Use power rule, product rule and quotient rule as needed.
- Find the second derivative.
- Find higher order derivatives.
- Solve velocity or acceleration problems.
- Apply the chain rule to find the derivative of composite algebraic functions.
- Apply the chain rule to find the derivative of composite trigonometric functions.
- Apply the chain rule to evaluate the derivative of composite functions.
- Apply the chain rule to solve word problems.
- Find dy/dx by implicit differentiation.
- Evaluate dy/dx at a given point.
- Find the second derivative in terms of x and y.
- Find the equations of tangent and normal lines to circles.
- Find the values of dx/dt or dy/dt.
- Solve related rate word problems for:
- Conic section forms,
- Right triangle forms,
- Angles of elevation,
- Linear vs angular speed.
- Cylinder forms
- Collected data types that require regression analysis.

### Chapter 3

- Find critical numbers.
- Use a graphing calculator to:
- Graph functions
- Use
*zoom*and*trace*features - Use
*calc*menu - Use the
*table*feature - Use the
*regression*capabilities - Locate absolute extrema.
- Solve word problems related to extrema.
- Locate intervals where a function is increasing or decreasing.
- Determine the effect the relationship between f and g has on f' and g'.
- Find relative extrema.
- Find points of inflection.
- Sketch graphs.
- Solve word problems using relative extrema.
- Find limits as x goes to ¥.
- Sketch/analyze graphs that may have asymptotes.
- Sketch/analyze graphs of algebraic functions.
- Sketch/analyze graphs of trigonometric functions.
- Solve minimum/ maximum word problems of type:
- Sum or product of numbers,
- Area or volume.
- Find the differential dy
- Use differentials to approximate error.
- Use differentials to approximate roots or powers.
- Find Marginals.
- Solve maximum profit problems.
- Solve minimum cost problems.
- Solve demand problems.

### Chapter 4

- Evaluate indefinite integrals,
- Algebraic
- Trigonometric.
- Solve differential equations.
- Solve word problems,
- Growth,
- Vertical motion,
- Acceleration.
- Find sums.
- Use sigma notation to write sums.
- Use properties of sigma notation to evaluate sums.
- Find the limit of s(n) as n --> ¥.
- Use upper and lower sums to approximate the area of a region.
- Use the limit process to find the area of a region between a function and the x-axis.
- Set up a definite integral that yields a given area.
- Sketch the region indicated by a given integral.
- Use geometric formulas to calculate area.
- Given values of definite integrals find the values of related definite integrals.
- Evaluate the definite integral by the limit definition.
- Express a limit as a definite integral.
- Evaluate definite integrals of
- Algebraic functions,
- Trigonometric functions.
- Determine the area of regions bounded by graphs.
- Integrate to find F(X).
- Use the Second Fundamental Theorem of Calculus to find F'(x).
- Identify u and du for a given integral.
- Evaluate indefinite integrals a) algebraic, b) trigonometric, c) radicals
- Evaluate definite integrals.

## Contact

Sunny Kang

Department Chair

Office: E321-D

Phone: 617-228-3367

ska14437@bhcc.mass.edu