By Bob Miller
The 1st calc research courses that actually provide scholars a clue.Bob Miller's student-friendly Calc for the Clueless positive factors quickly-absorbed, fun-to-use info and support. scholars will snap up Calc for the Clueless as they detect: * Bob Miller's painless and confirmed recommendations to studying Calculus * Bob Miller's means of awaiting difficulties * Anxiety-reducing positive factors on each web page * Real-life examples that deliver the maths into concentration * Quick-take tools tht healthy brief learn classes (and brief cognizance spans) * the opportunity to have a existence, instead of spend it attempting to decipher calc!
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Additional info for Bob Miller's Calc for the Clueless: Calc I
Finally we will learn, sadly, that most integrals cannot be done. As we go on in math, we will learn many approximation methods. Also, we will learn how accurate these approximations are. This is OK because we don't live in a perfect world—or is this a surprise to you? As we go on, the methods of approximation will become more involved. Let us take a look at some crude ones. We will approximate in three ways. Example 33— Approximate this integral with three equal subdivisions, using the right end of each one.
We get The definite integral. In the above example, the definite integral represents the area. As in the case of derivatives, we would like the rules so that it would be unnecessary to do this process of approximating rectangles. Note If the velocity = v(t), represents the distance traveled from time a to time b. Rule 6 Rule 7 Rule 8 Rule 9 Rule 10 Rule 11 Rule 12 The fundamental theorem of integral calculus. If f(x) is continuous on [a,b] and F(x) is any antiderivative of f(x), then Example 26— Note dx, the definite integral, is a number if a and b are numbers.
The sketch is... You should be getting a lot better now!! Let us try a polynomial, to show you how easy it is. Example 22— Intercepts: (0,0), (1,0), (2,0), (3,0), and (5,0). No asymptotes. Watch how easy this is! f(5 +) is negative. (5 - x)9 is an odd power, so cross. (x- 3)7 is an odd power, so cross. (x- 2)6 is an even power, no cross. (x- 1)5 is an odd power, so cross, x4 is an even power, no cross. The leading term, -X31, dominates when x is big (say x = 100) or when x is small (say x = -100).