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Calculus: Where are you?

Calculus: Where are you?. A. I’ve seen no calculus. B. I saw just a little in Pre-calculus. C. I’ve had less than a year. D. I’ve had a year. E. I’ve had more than a year. A QCQ (Quick Calculus Question).

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Calculus: Where are you?

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  1. Calculus: Where are you? • A. I’ve seen no calculus. • B. I saw just a little in Pre-calculus. • C. I’ve had less than a year. • D. I’ve had a year. • E. I’ve had more than a year.

  2. A QCQ (Quick Calculus Question) • What is the slope of the tangent line to the curve f (x) = x2 at the point (3, 9)? • A. 9 • B. 2x • C. 6 • D. 18 • E. Haven’t the foggiest

  3. Another QCQ • What is the area under the curve f (x) = x2 between x = 0 and x = 2? • A. 4 square units • B. 8/3 square units • C. 11/2 square units • D. 7 square units • E. I’m clueless

  4. Calculus – The Big Picture(1/21/09) • Calculus is the study of quantities which are changing. • These quantities are most often expressed as functions. • We may know a function and seek information about its rate of change, or conversely we may know about its rate of change and seek information about that function.

  5. Calculus: Limits, Derivatives, and Integrals • Given a function, its rate of change is called its derivative (Calc I). • Given a rate of change, its corresponding function is called an antiderivative (Calc I and II). • Given lots of values of a function, we can add them all up by using the integral (Calc I and II). • All of these concepts involve the concept of limit (Calc I).

  6. Some Sample Problems • Given a linear function, say y = 3 x + 1, what is its rate of change when x = 2? When x = 4? • Given a quadratic function, say y = x 2, what is its rate of change when x = 2? When x = 4? • Given an exponential function, say y = 2x, what is its rate of change when x = 2? When x = 4?

  7. More samples • What is the area below y = 3 x + 1 between x = 2 and x = 4? • What is the area below y = x2between x = 2 and x = 4? • What is the area below y = 2xbetween x = 2 and x = 4?

  8. A final clicker question today • Right now, I feel that MA 111 • A. is probably about right for me. • B. may be too hard – I’m worried about my preparation. • C. may be too easy - I may know most of this stuff already. • D. …. Not sure yet how I feel.

  9. Assignment for Friday • If you are unsure if MA 111 is right for you, go to http://www.skidmore.edu/academics/mcsand take thecalculus placement exam. You need your Skidmore username and password to access the exam. • You must decide by next Monday if you will stay in MA 111, or if you want to move up (113). No “down” is available in the spring. • Obtain the textbook and read To the Student (page xxiii) and A Preview of Calculus (pages 2-9).

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