- 3.5.1: Let f (x) = x2 1, 0 x 2 (a) Graph y = f (x) for 0 x 2. (b) Show tha...
- 3.5.2: Let f (x) = x3 2x + 3, 3 x 1 (a) Graph y = f (x) for 3 x 1. (b) Use...
- 3.5.3: Let f (x) = _ x2 + 2, 1 x 2 (a) Graph y = f (x) for 1 x 2. (b) Use ...
- 3.5.4: Let f (x) = sin x x, 1 x 1 (a) Graph y = f (x) for 1 x 1. (b) Use t...
- 3.5.5: Use the intermediate-value theorem to show that ex = x has a soluti...
- 3.5.6: Use the intermediate-value theorem to show that cos x = x has a sol...
- 3.5.7: Use the bisection method to find a solution of ex = x that is accur...
- 3.5.8: Use the bisection method to find a solution of cos x = x that is ac...
- 3.5.9: (a) Use the bisection method to find a solution of 3x3 4x2 x + 2 = ...
- 3.5.10: In Example 2, how many steps are required to guarantee that the app...
- 3.5.11: Suppose that the number of individuals in a population at time t is...
- 3.5.12: Suppose that the biomass of a population at time t is given by B(t)...
- 3.5.13: Explain why a polynomial of degree 3 has at least one root.
- 3.5.14: Explain why a polynomial of degree n, where n is an odd number, has...
- 3.5.15: Explain why y = x2 4 has at least two roots.
- 3.5.16: On the basis of the intermediate-value theorem, what can you say ab...
Solutions for Chapter 3.5: Properties of Continuous Functions
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series) | 3rd Edition
Characteristic polynomial of a square matrix A
det(xIn - A), where A is an n x n matrix
Combinations of n objects taken r at a time
There are nCr = n! r!1n - r2! such combinations,
A fractional expression in which the numerator or denominator may contain fractions
See Cartesian coordinate system.
The process of utilizing general information to prove a specific hypothesis
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant
Arrows that have the same magnitude and direction.
A procedure for fitting an exponential function to a set of data.
Any solution of the resulting equation that is not a solution of the original equation.
Higher-degree polynomial function
A polynomial function whose degree is ? 3
Inequality symbol or
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0
Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2
See Parametric equations.
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.
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.
Solve by substitution
Method for solving systems of linear equations.
Symmetric about the origin
A graph in which (-x, -y) is on the the graph whenever (x, y) is; or a graph in which (-r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is
Variable (in statistics)
A characteristic of individuals that is being identified or measured.
The function that associates points on the unit circle with points on the real number line