By Paul A. Foerster

The acclaimed Calculus: thoughts and purposes is now to be had in a brand new variation, revised to mirror very important alterations within the complicated Placement curriculum, and up-to-date to include suggestions from teachers through the united states With over forty years of expertise instructing AP Calculus, Paul Foerster built Calculus: recommendations and functions with the highschool scholar in brain, yet with the entire content material of a college-level path. just like the prior version, the second one version follows the AP Calculus curriculum for either AB and BC degrees. In Calculus: recommendations and functions, scholars start up with calculus! assessment of precalculus happens at quite a few issues while it’s wanted. The textual content combines graphing-calculator know-how with a different, real-world program technique, and offers calculus as a research of simply 4 basic ideas: limits, derivatives, certain integrals, and indefinite integrals. scholars study those recommendations utilizing algebraic, numerical, graphical, and verbal techniques. for that reason, scholars with a much broader diversity of skills might be profitable in calculus, not only those people who are powerful in algebra. The accompanying set of Explorations within the Instructor’s source publication, designed for cooperative team paintings, provides scholars hands-on event with new subject matters prior to they're officially brought. during this new version, derivatives of transcendental capabilities, similar premiums, in addition to zone and quantity purposes of the certain indispensable are brought past. also, the Instructor’s source ebook contains initiatives using the CBL™, The Geometer’s Sketchpad ®, and Fathom Dynamic records™ software program, giving scholars prolonged possibilities to discover and comprehend calculus extensive.

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**Extra info for Calculus: Concepts and Applications**

**Example text**

235947...? Do the average rates seem to be approaching this instantaneous rate as the second value of x approaches 2? Which concept of calculus is the instantaneous rate? Which concept of calculus is used to find the instantaneous rate? d. Mary Thon runs 200 m in 26 s! Her distance, d , in meters from the start at various times t , in seconds, is given in the table. Estimate her instantaneous velocity in m/s when t = 2, t = 18, and t = 24. For which time intervals did her velocity stay relatively constant?

The value of f(c) equals the limit of f(x) as x approaches c. The branches of the graph are “connected” by f(c). These examples lead to a formal definition of continuity. 46 © 2005 Key Curriculum Press Chapter 2: Properties of Limits DEFINITION: Continuity Continuity at a Point: Function f is continuous at x = c if and only if 1. f(c) exists, 2. f(x) exists, and 3. f(x) = f(c). Continuity on an Interval: Function f is continuous on an interval of x-values if and only if it is continuous at each value of x in that interval.

5. 7. 15. 7 16. 8 17. 3 18. 4 8. 9. 10. 11. 12. For Problems 19–24, a. Plot the graph on your grapher. How does the graph relate to Problems 13–18? b. Find the limit of the function as x approaches the given value. For Problems 13–18, photocopy or sketch the graph. For the point marked on the graph, use proper limit notation to write the limit of f(x). For the given value of , estimate to one decimal place the largest possible value of that you can use to keep f(x) within units of the marked point when x is within units of the value shown.