Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 76 ppsx

... (positive for f> 0and negative for f<0 )and use our knowledge of functions and their graphs, along with a bit of basic geometry, to approximate some definite integrals and evaluate others. 12 REMARK: ... relationship between v  g and v  c ? 6. Suppose we want to approximate  2 0 f(x)dx by partitioning the interval [0, 2] into n equal pieces and constructing left-...

Ngày tải lên: 05/07/2014, 18:20

... Guardino, Sara Anderson, Michael Boezi, Susan Laferriere, and Barbara Atkinson. And thanks to Elka Block and Frank Purcell, for their comments and suggestions. Finally, I want to thank the following ... Polynomial Functions and Their Graphs 391 ◆ EXPLORATORY PROBLEMS FOR CHAPTER 11: Functions and Their Graphs: Tinkering with Polynomials and Rational Functions 404...

Ngày tải lên: 05/07/2014, 18:20

... value of f at2is7. 2 f → 7 f(2)=7 The expression y = f(x)is shorthand for “y is the output of f corresponding to an input of x” and it is read “y equals f of x.” When we say y = f(x),wemean that ... chances are that you’re at a bus stop. The symbol takes on a life of its own when a Bostonian says, “I’ll take the ‘T’ downtown.” On the other hand, New Yorkers look for an “M”...

Ngày tải lên: 05/07/2014, 18:20

... (fg)(x), and  f g  (x), and find their domains. 39. f(x)=ax + b and g(x) = cx + d 40. f(x)=3x + 2and g(x) = 5x − 1 41. f(x)=2x + 3and g(x) =x 2 −1 42. f(x)= 3 x+1 and g(x) = 2x x−5 43. f(x)= √ x and ... There are many ways of decomposing functions. For instance, suppose h(x) = x 2 + 1 x 2 + 2 and we want to find f and g such that f(g(x))=h(x). Determine which of the f...

Ngày tải lên: 05/07/2014, 18:20

... use demand curves to express the relationship between the price of an item and the number of items demanded by consumers. Below is a demand curve for a certain good. q is the quantity of the ... points (π,3 )and (−π,5) 8. Passing through point ( √ 3, √ 2) and parallel to 3x − 4y = 7 9. Passing through the origin and perpendicular to πx − √ 3y = 12 10. x-intercept of √ π...

Ngày tải lên: 05/07/2014, 18:20

... unknown constants, a, b, and c. 5 If one of the points we know happens to be the vertex of the parabola (and we are aware of that), then the parabola is determined by just the vertex and one other ... opening upward; y =−x 2 is an example of a parabola opening downward. x = y 2 is an example of a parabola opening to the right, and x =−y 2 is an example of a parabo...

Ngày tải lên: 05/07/2014, 18:20

... graphing calculator. Your answers to parts (a) and (b) ought to agree with your answer to part (c). You can use your answers to parts (a) and (b) to select an appropriate viewing window in your calculator. i. ... 11.4 Rational Functions and Their Graphs 409 numerator and the denominator of the rational function. We will use the fact that for any positive integer n...

Ngày tải lên: 05/07/2014, 18:20

... price and quantity can both be thought of as functions of time. At a certain instant the price is $6 and is increasing at a rate of $0.25 per week. At what rate is the quantity demanded changing ... barrel stands upright and oil comes out a faucet at the base of the tank. (a) How are the volume of oil in the tank and the height of oil in the tank related? (b) What is the...

Ngày tải lên: 05/07/2014, 18:20

... 19.20 Between x = 0 and x = π/2, the numerator and denominator are positive. The numerator is increasing and the denominator is approaching zero, so tan x grows without bound. tan(−x) = sin(−x) cos(−x) = − ... A, B, and C are positive constants and y =A sin(Bx +C). What are the period and amplitude of the sine graph? Describe the horizontal shift. 19.3 The Function f(x)=tan x 61...

Ngày tải lên: 05/07/2014, 18:20

... “angle of elevation” and “angle of depression.” Angle of elevation refers to the angle from the horizontal up to an object; angle of depression refers to the angle from the horizontal down to an ... trigonometry to con- struct edifices and to estimate distances and heights—from estimating the height of the great Egyptian pyramids in Giza to estimating the size...

Ngày tải lên: 05/07/2014, 18:20