Barrons AP Calculus
The graphs of and g(x) = 3x^2 − 1 are shown in Figure N1–1; f(x) is odd, g(x) even. Figure N1–1 ...
interchange x and y, then solve for y. Example 6 __ Find the inverse of the one-to-one function f(x) = x^3 ...
(a) (b) (c) (d) three zeros, since x^4 − 2x^2 = x^2 (x^2 − 2) equals zero if x = 0, + , or −. B ...
Figure N1–4 SOLUTIONS: The graphs are shown in Figures N1–4a through N1–4d. Figure N1–4a Figure N1–4b ...
Figure N1–4c Figure N1–4d Note that graph (c) of y = −f(x) is the reflection of y = f(x) in the x-ax ...
(a) (b) (c) SOLUTIONS: y = f(x) See Figure N1–5a. Figure N1–5a y = |f(x)| See Figure N1–5b. Figure N1–5b y = f ...
Figure N1–5c Note how the graphs for (b) and (c) compare with the graph for (a). C. POLYNOMIAL AND OTHER RATIONAL ...
(a) (b) (a) (b) (c) (d) given in the Appendix. D1. Periodicity and Amplitude Trigonometric functions The trigonometric f ...
(a) (b) (c) (d) The period of f is , or 6. Since the maximum value of −sin x is −(−1) or +1, the maximum v ...
Figure N1–7 Also, for other inverse trigonometric functions, y = cos−1 x (or arccos x) has domain −1 x 1 and ...
= e x, where e is an irrational number whose decimal approximation to five decimal places is 2.71828. ...
set of positive reals; its range is the set of all reals. The graphs of the mutually inverse functions ln x and ...
Figure N1–9 Note that, as t increases from 0 to 2π, a particle moving in accordance with the given ...
Figure N1–10 The function defined by the parametric equations here is , whose graph is at the right ab ...
Figure N1–11 Example 15 __ Graph x = y 2 − 6y + 8. SOLUTION: We encounter a difficulty here. The calc ...
SOLUTION: Recalling that f −1 interchanges x and y, we use parametric mode to graph f: x = t, y = t ...
(a) (b) (a) (b) BC ONLY Example 17 __ Consider the polar function r = 2 + 4 sin θ. For what values of θ ...
Figure N1–15 A polar function may also be expressed parametrically: x = r cos θ, y = r sin θ In this ...
CHAPTER SUMMARY This chapter has reviewed some important precalculus topics. These topics are ...
(A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) PRACTICE EXERCISES Directions: Answer Questions 1 ...
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