Barrons AP Calculus - David Bock

(b) When is the object moving to the left? (c) Give one value of t from the interval in part (b) at which the speed of the objec ...

L(t) (ft^3 /min)^47986520 (a) Estimate L ′(15). (b) Explain in this context what your answer to part a means. (c) The falling gr ...

(a) Find A(6) and A(18). (b) What is the average value of f on the interval 0 ≤ x ≤ 18? (c) Write the equation of the line tange ...

TOPICAL REVIEW AND PRACTICE ...

CHAPTER 1 Functions Concepts and Skills In this chapter you will review precalculus topics. Although these topics are not direct ...

Find the domains of: SOLUTIONS: (a) The domain of is the set of all reals except x = 1 (which we shorten to “x ≠ 1”). (b) The do ...

A4. A function f is if, for all x in the domain of f, The graph of an odd function is symmetric about the origin; the graph of a ...

FIGURE N1–2 Note that the graphs of f and f −1 in Figure N1–2 are mirror images, with the line y = x as the mirror. A7. The zero ...

(a) Sketch the graph of y = |f (x)|. (b) Sketch the graph of y = f (|x|). (c) Sketch the graph of y = − f (x). (d) Sketch the gr ...

FIGURE N1–4c FIGURE N1–4d Note that graph (c) of y = − f (x) is the reflection of y = f (x) in the x-axis, whereas graph (d) of ...

FIGURE N1–5a (b) y = |f (x)| See Figure N1–5b. FIGURE N1–5b (c) y = f (|x|) See Figure N1–5c. FIGURE N1–5c Note how the graphs f ...

of the polynomial is n. A linear function, f (x) = mx + b, is of the first degree; its graph is a straight line with slope m, th ...

SOLUTIONS: (a) The period of f is or 6. (b) Since the maximum value of −sin x is −(−1) or +1, the maximum value of f is 3 + 1 or ...

FIGURE N1–7 Also, for other inverse trigonometric functions, y = cos−1 x (or arccos x) has domain −1 x 1 and range 0 y π; y = ta ...

as can be seen in Figure N1–8. FIGURE N1–8 The logarithmic function log a x (a > 0, a ≠ 1) has the following properties: The ...

Since sin^2 t + cos^2 t = 1, we have The curve is the ellipse shown in Figure N1–9. FIGURE N1–9 Note that, as t increases from 0 ...

FIGURE N1–10 The function defined by the parametric equations here is y = F(x) = whose graph is at the right above; its domain i ...

interchange. Less risky and more satisfying is to switch to parametric mode: Enter x = t^2 − 6t + 8 and y = t. Then graph these ...

FIGURE N1–14 A polar function defines a curve with an equation of the form r = f ( ). Some common polar functions include: EXAMP ...

A polar function may also be expressed parametrically: x = r cos , y = sin In this form, the curve r = 2 + 4 sin from Example 17 ...