- 9.1: (a) A direction field for the differential equation is shown. Sketc...
- 9.2: (a) Sketch a direction field for the differential equation . Then u...
- 9.3: (a) A direction field for the differential equation is shown. Sketc...
- 9.4: (a) Use Eulers method with step size 0.2 to estimate , where is the...
- 9.5: Solve the differential equation.
- 9.6: Solve the differential equation.
- 9.7: Solve the differential equation.
- 9.8: Solve the differential equation.
- 9.9: Solve the initial-value problem
- 9.10: Solve the initial-value problem
- 9.11: Solve the initial-value problem
- 9.12: Solve the initial-value problem , , and graph the solution.
- 9.13: Find the orthogonal trajectories of the family of curves
- 9.14: Find the orthogonal trajectories of the family of curves
- 9.15: (a) Write the solution of the initial-value problem and use it to f...
- 9.16: (a) The population of the world was 5.28 billion in 1990 and 6.07 b...
- 9.17: The von Bertalanffy growth model is used to predict the length of a...
- 9.18: A tank contains 100 L of pure water. Brine that contains 0.1 kg of ...
- 9.19: One model for the spread of an epidemic is that the rate of spread ...
- 9.20: The Brentano-Stevens Law in psychology models the way that a subjec...
- 9.21: The transport of a substance across a capillary wall in lung physio...
- 9.22: Populations of birds and insects are modeled by the equations (a) W...
- 9.23: Suppose the model of Exercise 22 is replaced by the equations (a) A...
- 9.24: Barbara weighs 60 kg and is on a diet of 1600 calories per day, of ...
- 9.25: When a flexible cable of uniform density is suspended between two f...
Solutions for Chapter 9: Single Variable Calculus 7th Edition
Full solutions for Single Variable Calculus | 7th Edition
See Inverse tangent function.
A matrix that represents a system of equations.
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.
A function that is continuous on its entire domain
See Polar coordinates.
For the equation ax 2 + bx + c, the expression b2 - 4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2 - 4AC
Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x ) - x 2)2 + (y1 - y2)2 + (z 1 - z 2)2
equation of a parabola
(x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h)
Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .
Identity involving a trigonometric function of u/2.
Using the science of statistics to make inferences about the parameters in a population from a sample.
Point where a curve crosses the x-, y-, or z-axis in a graph.
Length of an arrow
See Magnitude of an arrow.
A pair of real numbers (x, y), p. 12.
The closest point to the Sun in a planet’s orbit.
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,
The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.
A set of points in Cartesian space equally distant from a fixed point called the center.
A letter that represents an unspecified number.
x = a.