Barrons AP Calculus
(A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) Assume that the density of vehicles (number per mile) during ...
(B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) 650,000 691,200 702,000 850, ...
(C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) 2.25 3 3.083 Water is leaking from a tank at the rat ...
(A) (B) (C) (D) (E) 30. (A) (B) (C) (D) (E) 31. (A) (B) (C) (D) (E) Approximately when did the 200th visitor go to this ...
■ ■ ■ ■ ■ ■ 9 Differential Equations CONCEPTS AND SKILLS In this chapter, we review how to write and solve ...
Differential equation A differential equation (d.e.) is any equation involving a derivative. In §E of Chap ...
Rate of Change A differential equation contains derivatives. A derivative gives information about the rate ...
curve is equal to its y-coordinate. Since the d.e. says that y is a function whose derivative is al ...
Figure N9–1b Figure N9–1c is the slope field for the d.e. . Slopes at many points are represent ...
(a) (b) (a) The slope field for the d.e. is shown in Figure N9–2. Carefully draw the solution curve th ...
(b) Figure N9–2b Since we already know that, if , then , we are assured of having found the correct general ...
Figure N9–3b Figure N9–3c Figure N9–3d SOLUTIONS: (A) goes with Figure N9–3c. The solution curves in the family ...
(a) (b) (a) (b) (B) goes with Figure N9–3a. The general solution is the family of parabolas y = x^2 + C. ...
point. This circle is not differentiable at (−5,0) and (5,0). (The d.e. shows undefined when y = 0, an ...
(a) (b) (c) Derivatives of Implicitly Defined Functions In Examples 2 and 3 above, each d.e. was of the form ...
Figure N9–5 ...
BC ONLY C. EULER’S METHOD In §B we found solution curves to first-order differential equations graphically, us ...
BC ONLY Example 6 __ Let . Use Euler’s method to approximate the y-values with four steps, star ...
The table gives us the numerical solution of using Euler’s method. Figure N9−6a shows the graphical solut ...
BC ONLY Figure N9–6a Figure N9–6b ...
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