 2.5.1E: In Exercises 1–4, say whether the function graphed is continuous on...
 2.5.2E: In Exercises 1–4, say whether the function graphed is continuous on...
 2.5.3E: In Exercises 1–4, say whether the function graphed is continuous on...
 2.5.4E: In Exercises 1–4, say whether the function graphed is continuous on...
 2.5.5E: Exercises 5–10 refer to the function graphed in the accompanying fi...
 2.5.6E: Exercises 5–10 refer to the function graphed in the accompanying fi...
 2.5.7E: Exercises 5–10 refer to the function graphed in the accompanying fi...
 2.5.8E: Exercises 5–10 refer to the function graphed in the accompanying fi...
 2.5.9E: Exercises 5–10 refer to the function graphed in the accompanying fi...
 2.5.10E: Exercises 5–10 refer to the function graphed in the accompanying fi...
 2.5.11E: At which points do the functions in Exercises 11 and 12 fail to be ...
 2.5.12E: At which points do the functions in Exercises 11 and 12 fail to be ...
 2.5.13E: At what points are the functions in Exercises 13–30 continuous?
 2.5.14E: At what points are the functions in Exercises 13–30 continuous?
 2.5.15E: At what points are the functions in Exercises 13–30 continuous?
 2.5.16E: At what points are the functions in Exercises 13–30 continuous?
 2.5.17E: At what points are the functions in Exercises 13–30 continuous?y = ...
 2.5.18E: At what points are the functions in Exercises 13–30 continuous?
 2.5.19E: At what points are the functions in Exercises 13–30 continuous?
 2.5.20E: At what points are the functions in Exercises 13–30 continuous?
 2.5.21E: At what points are the functions in Exercises 13–30 continuous?y = ...
 2.5.22E: At what points are the functions in Exercises 13–30 continuous?
 2.5.23E: At what points are the functions in Exercises 13–30 continuous?
 2.5.24E: At what points are the functions in Exercises 13–30 continuous?
 2.5.25E: At what points are the functions in Exercises 13–30 continuous?
 2.5.26E: At what points are the functions in Exercises 13–30 continuous?
 2.5.27E: At what points are the functions in Exercises 13–30 continuous?y = ...
 2.5.28E: At what points are the functions in Exercises 13–30 continuous?y = ...
 2.5.29E: At what points are the functions in Exercises 13–30 continuous?
 2.5.30E: At what points are the functions in Exercises 13–30 continuous?
 2.5.31E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.32E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.33E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.34E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.35E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.36E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.37E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.38E: Find the limits in Exercises 31–38. Are the functions continuous at...
 2.5.39E: Define g(3) in a way that extends g(x) = (x2 – 9)/(x – 3) to be con...
 2.5.40E: Define h(2) in a way that extends h(t) = (t2 + 3t – 10)/(t – 2) to ...
 2.5.41E: Define ƒ(1) in a way that extends ƒ(s) = (s3 – 1)/(s2 – 1) to be co...
 2.5.42E: Define g(4) in a way that extendsg(x) = (x2 – 16)/(x2  3x – 4)to b...
 2.5.43E: For what value of a is continuous at every x?
 2.5.44E: For what value of b is continuous at every x?
 2.5.45E: For what values of a is continuous at every x?
 2.5.46E: For what value of b is continuous at every x?
 2.5.47E: For what values of a and b is continuous at every x?
 2.5.48E: For what values of a and b is continuous at every x?
 2.5.49E: In Exercises 49–52, graph the function ƒ to see whether it appears ...
 2.5.50E: In Exercises 49–52, graph the function ƒ to see whether it appears ...
 2.5.51E: In Exercises 49–52, graph the function ƒ to see whether it appears ...
 2.5.52E: In Exercises 49–52, graph the function ƒ to see whether it appears ...
 2.5.53E: A continuous function y = ƒ(x) is known to be negative at x = 0 and...
 2.5.54E: Explain why the equation cos x = x has at least one solution.
 2.5.55E: Roots of a cubic Show that the equation x3  15x + 1 = 0 has three ...
 2.5.56E: A function value Show that the function F(x) = (x – a)2. (x – b)2 +...
 2.5.57E: Solving an equation If ƒ(x) = x3  8x + 10, show that there are val...
 2.5.58E: Explain why the following five statements ask for the same informat...
 2.5.59E: Removable discontinuity Give an example of a function ƒ(x) that is ...
 2.5.60E: Nonremovable discontinuity Give an example of a function g(x) that ...
 2.5.61E: A function discontinuous at every pointa. Use the fact that every n...
 2.5.62E: If functions ƒ(x) and g(x) are continuous for 0 ? x ? 1, could ƒ(x)...
 2.5.63E: If the product function h(x) = ƒ(x) . g(x) is continuous at x = 0 m...
 2.5.64E: Discontinuous composite of continuous functions Give an example of ...
 2.5.65E: Neverzero continuous functions Is it true that a continuous functi...
 2.5.66E: Stretching a rubber band Is it true that if you stretch a rubber ba...
 2.5.67E: A fixed point theorem Suppose that a function ƒ is continuous on th...
 2.5.68E: The signpreserving property of continuous functions Let ƒ be defin...
 2.5.69E: Prove that ƒ is continuous at c if and only if
 2.5.70E: Use Exercise 69 together with the identitiessin (h + c) = sin h cos...
 2.5.71E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
 2.5.72E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
 2.5.73E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
 2.5.74E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
 2.5.75E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
 2.5.76E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
 2.5.77E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
 2.5.78E: Use the Intermediate Value Theorem in Exercises 71–78 to prove that...
Solutions for Chapter 2.5: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 2.5
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. Chapter 2.5 includes 78 full stepbystep solutions. Since 78 problems in chapter 2.5 have been answered, more than 57772 students have viewed full stepbystep solutions from this chapter.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Bearing
Measure of the clockwise angle that the line of travel makes with due north

Categorical variable
In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

Closed interval
An interval that includes its endpoints

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Horizontal component
See Component form of a vector.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Inverse function
The inverse relation of a onetoone function.

Linear system
A system of linear equations

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Parametric curve
The graph of parametric equations.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Vertical component
See Component form of a vector.