By Bob Miller
The 1st calc learn publications that actually supply scholars a clue.Bob Miller's student-friendly Calc for the Clueless good points quickly-absorbed, fun-to-use info and aid. scholars will snap up Calc for the Clueless as they notice: * Bob Miller's painless and confirmed concepts to studying Calculus * Bob Miller's means of waiting for difficulties * Anxiety-reducing positive aspects on each web page * Real-life examples that convey the mathematics into concentration * Quick-take tools tht healthy brief examine periods (and brief recognition spans) * the opportunity to have a existence, instead of spend it attempting to decipher calc!
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Extra resources for Bob Miller's Calc for the Clueless: Calc I
Example 4— A box has a square base and no top. A. Find the minimum surface area needed if the volume is 4 cubic feet. Let's also do the related problem— B. Find the maximum volume if the surface area is 12 square feet. As before, the volume = (1)(w)(h). With a square base, V = x2y. A box with no top has five surfaces—a square bottom and four sides, all of which have the same dimensions. The surface area S = x2 + 4xy. Let's do A. The box is 2 by 2 by 1 feet. S = x 2 + 4xy = (2)2 + 4(2)(1) = 12 square feet.
Oblique asymptote. We must, unfortunately, long divide the bottom into the top. If you know it, use synthetic division. As x goes to infinity, the remainder 21/(x + 4) goes to 0. The oblique asymptote is y = x - 6. Note 1 If the degree of the top is more than the bottom but not 1, there are no oblique asymptotes. Note 2 At most there is one oblique asymptote or one horizontal asymptote, but not both. There might be neither. Curve Sketching By the Pieces Before we take a long example, we will examine each piece.
If so, don't look at what follows. Intercepts: (0,0), (3,0). Max, min: (0,0) is the max, (2,-4) is the min. Inflection point: (1,-2). Right end to plus infinity and left end to minus infinity. Polynomials have no asymptotes. And the sketch is... Answers Answers to the problem on page 68: x A B C D E F G H I J K f(x) - - + 0 ? - 0 + + + + f'(x) + ? 0 - ? + + - 0 ? - f"(x) 0 ? - - ? 0 + + + ? 0 Chapter 4 Word Problems Made Easy ... Well, Less Difficult Word problems are not difficult because of the calculus.