Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 45 pdf

... = x+1 x−2 . We interchange the input and output (x and y) to obtain f −1 . PART IV Inverse Functions: A Case Study of Exponential and Logarithmic Functions 12 CHAPTER Inverse Functions: Can What Is Done ... function g(x) and verify that f(g(x))=I(x )and g(f (x)) = I(x). (a) f(x)=6x −3 (b) f(x)=(x − 3) 3 3. On the same set of axes, sketch the graphs of the following pair...

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... change with constant rate of change, 712–714 difference between left- and right-hand sums and, 718–722 explanation of, 712 with nonconstant rate of change, 715–718 overview of, 711–712 Newton, ... rates of change and, 550–554 Improper integrals explanation of, 903 infinite interval of integration and, 903–907 method of comparison and, 912–914 methods to approach, 9...

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... heights of the graphs of f and g at x 1 .An analogous statement can be made for subtraction. The domain of h is the set of all x common to the domains of both f and g. ◆ EXAMPLE 3.2 Let f(x)=x and ... sum of functions f and g, h(x) = f(x)+g(x), then the output of h corresponding to an input of x 1 is the sum of f(x 1 )and g(x 1 ). In terms of the graphs...

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... a horizontal asymptote, be sure that (degree of the numerator) < (degree of the denominator). For any other horizontal asymptote, the degree of the numerator and denominator must be equal; ... from t = 1tot=5? If so, find that time. (c) On the same set of axes, illustrate your answers to parts (a) and (b). 11.4 Rational Functions and Their Graphs 411 The graph will look...

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... The rate of change of the amount of money is 10% of the amount of money. Frequently scientists have knowledge about the rate of change of a quantity and from this (and one piece of data about amount—like ... of each of these stocks at the beginning of the year? 4. Compute the following limits. In each case stop to think of a strategy, and use whatever strategy s...

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... x −→ ←− arcsin x range of sine [−1, 1] domain of arcsine domain of tangent (−π/2, π/2) range of arctangent tan x −→ ←− arctan x range of tangent (−∞, ∞) domain of arctangent The Inverse Trigonometric Functions Definition sin −1 x ... all x in the domain of cos −1 x. On most calculators the arcsine and sine functions share a key, the arccosine and cosine functions share...

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... infinitely many correct answers.) Give an exact answer in terms of t ∗ . 20.5 APPLYING TRIGONOMETRY TO A GENERAL TRIANGLE: THE LAW OF COSINES AND THE LAW OF SINES We began our study of triangle trigonometry ... knows the distance from his ship to port A, the distance from his ship to port B, and the distance between the two ports. Due to weather conditions he wants to c...

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... between Dante and Anthony, 30 yards between Dante and Cliff, and 40 yards between Anthony and Cliff. Dante fakes a pass to Anthony but throws the ball instead to Cliff. Through what angle must ... lengths of the unidentified sides and the measures of the unidentified angles. Round off your answers to the nearest tenth. 5. After a hurricane a tree is left standing but makes...

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... added to the tank between t = 0 and t = 1 less than, greater than, or equal to the amount lost between t = 4 and t = 5? (Try to answer without doing any computations.) 24.2 The Average Value of ... Calculus becomes transparent. Because any two antiderivatives of f differ only by an additive constant and the con- stants will cancel in the course of subtraction, it follows t...

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... and left-hand sums to approximate  b a f(t)dt.Wepartition the interval [a, b] into n equal pieces each of length t. Let R n be the right-hand sum using n subdivisions and L n be the left-hand ... show an alternative and more efficient method of using the trapezoidal and midpoint sums to approximate this integral. ◆ Numerical methods of integration, such as left- and rig...

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