Calculus for the Utterly Confused

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McGraw Hill Professional, Jul 22, 1998 - Mathematics - 208 pages
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When it comes to understanding one of your most intimidating courses--calculus--even good students can be confused. Intended primarily for the non-engineering calculus student (though the more serious calculus student will also benefit), Calculus for the Utterly Confused is your ticket to success. Calculus concepts are explained and applied in such diverse fields as business, medicine, finance, economics, chemistry, sociology, physics, and health and environmental sciences. The message of Calculus for the Utterly Confused is simple: You donŐt have to be confused anymore. With the wealth of expert advice from the authors who have taught many, many confused students, youŐll discover a newer, fresher, clearer way to look at calculus. DonŐt wait another minute--get on the road to higher grades and greater confidence, and go from utterly confused to totally prepared in no time!
 

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Contents

Mathematical Background
1
Limits and Continuity
27
Derivatives
33
Graphing
45
MaxMin Problems
57
Related Rate Problems
65
Integration
75
Trigonometric Functions
105
Exponents and Logarithms
131
More Integrals
155
Mathematical Tables
181
Index
187
Copyright

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Page 62 - The strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from a circular cylindrical log of radius r.
Page 87 - Find the area under the curve y = x2 between x = 0 and x = 2 . Solution: Graph the curve as shown in Fig.
Page 39 - ... this sort if we imagine a relation of the first degree to hold between the displacement of a particle, its velocity, and its acceleration, the coefficients of the equation depending in an arbitrary manner upon the time. The particular equation that we have just defined is of the second order, because the velocity is the first derivative, and the acceleration is the second derivative, of the displacement; but we can imagine linear equations where derivatives appear of any order, and which are...
Page 42 - Jt4 +x2y2 -xy3 =18 where it is impossible to solve for x in terms of y or y in terms of x.
Page 37 - Table 4-2), and make the general statement that the derivative of a sum of terms is the sum of the derivatives of the individual terms. In...
Page 33 - LIMIT 87 of continuous functions, and the above definition is narrow because it excludes many limits of continuous functions. When the limit of a function at a point exists and is equal to the value of the function at that point, then we say the function is continuous at the point in question; that is, the variable function, which is continuous at every point, passes continuously without jumps from one value to another. The definition quoted above of a limit is inconsistent with our idea of continuity...
Page 5 - Take 1/2 of the x coefficient, square it, and add to both sides of the equation. This makes the left side a perfect | pattern square and the right side a number.
Page 108 - Each degree is further subdivided into 60 minutes, and each minute into 60 seconds.

About the author (1998)

McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide

McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide

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