- 6.1: The differential equationwhere and are positive constants, is calle...
- 6.2: A thermometer is taken from a room at to the outdoors, where the te...
- 6.3: Let represent sales of a new product (in thousands of units), let r...
- 6.4: Another model that can be used to represent population growth is th...
- 6.5: Show that the logistic equationcan be written asWhat can you conclu...
- 6.6: Torricellis Law states that water will flow from an opening at the ...
- 6.7: The cylindrical water tank shown in the figure has a height of 18 f...
- 6.8: Suppose the tank in Exercise 7 has a height of 20 feet, a radius of...
- 6.9: In hilly areas, radio reception may be poor. Consider a situation w...
- 6.10: Biomass is a measure of an amount of living matter in an ecosystem....
- 6.11: If the tracer is injected instantaneously at time then the concentr...
- 6.12: Use the solution of the differential equation in Exercise 11 to fin...
- 6.13: In Exercises 11 and 12, it was assumed that there was a single init...
Solutions for Chapter 6: Calculus of a Single Variable 8th Edition
Full solutions for Calculus of a Single Variable | 8th Edition
Difference of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
Differentiable at x = a
Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.
The left side of u(v + w) = uv + uw.
Identity involving a trigonometric function of u/2.
Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.
Initial side of an angle
Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.
Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)
A procedure for fitting a logistic curve to a set of data
Angle measure equal to 1/60 of a degree.
The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).
A function that assigns real-number values to the outcomes in a sample space.
Any number that can be written as a decimal.
Stemplot (or stem-and-leaf plot)
An arrangement of a numerical data set into a specific tabular format.
See Horizontal translation, Vertical translation.
The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.