Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 37 pot
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 37 pot
... 1] Figure 10.10 We’ll refer to the set of points we need to sieve through in order to identify extrema as candidates for extrema or candidates for maxima and minima. We can summarize our observations ... the amount of material required to construct a can of a given volume? Example 6.1 was such an optimization problem; a gardener had a fixed amount of fencing and wanted t...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 9 potx
... undefined and discontinuous at x = 0. (e) j is 1 -to- 1. Answers to Exercise 2.8 (a) g and h are even functions. (b) f and j are odd functions. (c) The graph of an odd function is said to have symmetry ... Characterizing Functions and Introducing Rates of Change Definition A is inversely proportional to B if A = k B for some constant k. As B increases A decreases,...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 20 potx
... f(a) )and (b, f(b)). The instantaneous rate of change of f at x = a can be approximated by the average rate of change of f on [a, a + h] for h very close to zero. As h gets closer and closer to ... rate of change over the tiny interval approaches the instantaneous rate of change at x = a. The instantaneous rate of change of f at x = a ≈ f(a +h) − f(a) (a + h) − a for h...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 26 potx
... equation of the parabola with the specifications given. 17. x-intercepts of 3 and −2; maximum value of 1 18. x-intercepts of π and 3π; y-intercept of 6 19. x-intercepts of π and 3π; y-intercept of −2 20. ... (i) and three arbitrary points we can obtain a system of three linear equations that we can solve for the constants a, b, and c. We can use the x-intercepts r 1...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 35 potx
... Animals eat plants and so have the same ratio of C 14 to C 12 as do the plants and the atmosphere. Thus, during the lifetime of a living organism the ratio of C 14 to C 12 in the organism is fixed; ... sketch the graphs of f(x)=2 x ,g(x) = 3 x , and h(x) = 10 x . Then, on another set of axes, draw a rough sketch of the graphs of f (x), g (x), and h (x). The grap...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 36 potx
... chances of winning? (e) Sketch a graph of P (n). Use [0, 100] as the range of the graph. Explain the practical significance of any asymptotes. 9.4 THE DERIVATIVE OF AN EXPONENTIAL FUNCTION As an ... average or at instantaneous rates of change, we can state the following. Exponential functions grow at a rate proportional to themselves. Exponential functions have a cons...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 49 potx
... Logarithmic and Exponential Functions We are looking for the slope of the tangent line to ln x at x = b. Let L 1 be the tangent line to e x at (c, b) and L 2 be the tangent line to ln x at (b, ... slope at any point on the graph of e x is given by the y-coordinate of that point), the slope of the tangent line to e x at (c, b)isb.Since the roles of x and y are interch...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 50 pot
... combination of these differentiation formulas and the laws of logs and exponents. The main piece of advice is to spend time 480 CHAPTER 14 Differentiating Logarithmic and Exponential Functions REMARK ... to solve e x − x = 5 alge- braically to see what this means. If we want to estimate the solutions, we can do so using a graphing calculator. At this point, we should kno...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 55 potx
... instantaneous rate of change of y with respect to x at x = 2. Notation: y , f , f (x), y (x), dy dx , df dx all mean the same thing. d dx is an operator that means “take the derivative of ... They can get to the store by a combination of boat and foot. Where should they build their dock so the commute to the store takes the minimum amount of time? home 6 miles R...
Ngày tải lên: 05/07/2014, 18:20
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 65 pot
... pointer of the second hand travel when the second hand travels through an angle of 70 ◦ ? 19.4 Angles and Arc Lengths 621 (1, 0); the line drawn from the origin to (0, 1) makes an angle of π 2 radians ... 19.22 Radians are unitless. When we write sin(1.1) and want to think of 1.1 as an angle, then it is an angle in radians. In other words, sin(1.1) = sin(1.1 radians)....
Ngày tải lên: 05/07/2014, 18:20