- 7-5.Q1: If dy/dx is directly proportional to y, then dy/dx = ?.
- 7-5.1: How Eulers Method Works, 1: Figure 7-5e shows the slope field for t...
- 7-5.Q2: If dy/dx = 3y, then the general solution for y is ?.
- 7-5.2: How Eulers Method Works, 2: Figure 7-5f shows the slope field for t...
- 7-5.Q3: If dy/dx = 0.1 xy, what is the slope of the slope-field line at the...
- 7-5.3: For 3 and 4, the table shows values of the derivative dy/dx for a f...
- 7-5.Q4: If y = Ce0.2x and y = 100 when x = 0, then C = ?
- 7-5.4: For 3 and 4, the table shows values of the derivative dy/dx for a f...
- 7-5.Q5: dv/(1 v) = ?
- 7-5.5: Numerical Program for Eulers Method: Obtain or write a program for ...
- 7-5.Q6: (d/dx)(sec x) = ?
- 7-5.6: Graphical Program for Eulers Method: Obtain or write a grapher prog...
- 7-5.Q7: Sketch the graph of y for Figure 7-5d. Figure 7-5d
- 7-5.7: Figure 7-5g shows the slope field for the differential equation Fig...
- 7-5.Q8: Differentiate implicitly: x3y5 = x + y
- 7-5.8: Figure 7-5h shows the slope field for the differential equation Fig...
- 7-5.Q9: If f(x) = f(4), then f is ? at x = 4.
- 7-5.9: Escape Velocity Eulers Method: In of Section 7-4, you learned that ...
- 7-5.Q10: If f(x) = (3t + 5)4 dt, then (x) = ?. A. (3x + 5)4 B. 12(3x + 5)3 C...
- 7-5.10: Terminal Velocity Eulers Method: In of Section 7-4, you assumed tha...
- 7-5.11: overestimates of her velocity? How can you tell? c. When dv/dt reac...
- 7-5.12: Eulers Method for a Restricted Domain Problem: Figure 7-5k shows th...
- 7-5.13: Figure 7-4n a. What does the slope appear to be at the point (5, 12...
Solutions for Chapter 7-5: Graphical Solution of Differential Equations by Using Slope Fields
Full solutions for Calculus: Concepts and Applications | 2nd Edition
Solutions for Chapter 7-5: Graphical Solution of Differential Equations by Using Slope FieldsGet Full Solutions
Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal
The set of points on the “edge” of a region
Trigonometric functions when applied to real numbers are circular functions
A matrix whose elements are the coefficients in a system of linear equations
Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists
Direction angle of a vector
The angle that the vector makes with the positive x-axis
Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row
The behavior of a graph of a function as.
equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)
An equation written with exponents instead of logarithms.
An interval that does not include its endpoints.
See Polar coordinate system.
Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.
The principle of experimental design that makes it possible to use the laws of probability when making inferences.
The function ƒ(x) = 1x
Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.
Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.
A set of ordered pairs of real numbers.
Semiperimeter of a triangle
One-half of the sum of the lengths of the sides of a triangle.