- 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
A matrix that represents a system of equations.
Combinations of n objects taken r at a time
There are nCr = n! r!1n - r2! such combinations,
The function y = cot x
Domain of a function
The set of all input values for a function
Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.
Inequality symbol or
Inverse sine function
The function y = sin-1 x
Logarithmic re-expression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression
An interval that does not include its endpoints.
Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random
The graph in three dimensions of a seconddegree equation in three variables.
A variable (in statistics) that takes on numerical values for a characteristic being measured.
See Complex plane.
Sample standard deviation
The standard deviation computed using only a sample of the entire population.
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.
Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.
A letter that represents an unspecified number.
A point that lies on both the graph and the x-axis,.
The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.
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