- 9.3.1: Sketch three solution curves for each of the slope fields in Figure...
- 9.3.2: Sketch the slope field for dy/dx = y2 at the points marked in Figur...
- 9.3.3: Sketch the slope field for dy/dx = x/y at the points marked in Figu...
- 9.3.4: Figure 9.20 is a slope field for dy/dx = y 10. (a) Draw the solutio...
- 9.3.5: Figure 9.21 is the slope field for the equation y = x+y. (a) Sketch...
- 9.3.6: (a) For dy/dx = x2y2, find the slope at the following points: (1, 0...
- 9.3.7: Match the slope fields in Figure 9.22 with their differential equat...
- 9.3.8: Match the slope fields in Figure 9.23 with their differential equat...
- 9.3.9: Which one of the following differential equations best fits the slo...
- 9.3.10: (a) Consider the slope field for dy/dx = xy. What is the slope of t...
- 9.3.11: For 1116, consider a solution curve for each of the slope fields in...
- 9.3.12: For 1116, consider a solution curve for each of the slope fields in...
- 9.3.13: For 1116, consider a solution curve for each of the slope fields in...
- 9.3.14: For 1116, consider a solution curve for each of the slope fields in...
- 9.3.15: For 1116, consider a solution curve for each of the slope fields in...
- 9.3.16: For 1116, consider a solution curve for each of the slope fields in...
- 9.3.17: The Gompertz equation, which models growth of animal tumors, is y =...
Solutions for Chapter 9.3: SLOPE FIELDS
Full solutions for Applied Calculus | 5th Edition
Average rate of change of ƒ over [a, b]
The number ƒ(b) - ƒ(a) b - a, provided a ? b.
A variable that affects a response variable.
Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2 - x 1, y2 - y19>
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.
A function whose domain is the set of all natural numbers.
Notation used to specify intervals, pp. 4, 5.
See Numerical derivative of ƒ at x = a.
See Linear programming problem.
Real numbers shown to the right of the origin on a number line.
Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,
Range of a function
The set of all output values corresponding to elements in the domain.
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.
Angle measure equal to 1/60 of a minute.
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically
Stretch of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.
Symmetric property of equality
If a = b, then b = a
A point that lies on both the graph and the x-axis,.
The x-value of the right side of the viewing window,.