 2.4.1: Write an equation that expresses the fact that a function is contin...
 2.4.2: If is continuous on , what can you say about its graph?
 2.4.3: (a) From the graph of , state the numbers at which is discontinuous...
 2.4.4: From the graph of , state the intervals on which is continuous.
 2.4.5: Sketch the graph of a function that is continuous except for the st...
 2.4.6: Sketch the graph of a function that is continuous except for the st...
 2.4.7: Sketch the graph of a function that is continuous except for the st...
 2.4.8: Sketch the graph of a function that is continuous except for the st...
 2.4.9: A parking lot charges $3 for the rst hour (or part of an hour) and ...
 2.4.10: Explain why each function is continuous or discontinuous. (a) The t...
 2.4.11: If and are continuous functions with and , nd .
 2.4.12: Use the denition of continuity and the properties of limits to show...
 2.4.13: Use the denition of continuity and the properties of limits to show...
 2.4.14: Use the denition of continuity and the properties of limits to show...
 2.4.15: Explain why the function is discontinuous at the given number . Ske...
 2.4.16: Explain why the function is discontinuous at the given number . Ske...
 2.4.17: Explain why the function is discontinuous at the given number . Ske...
 2.4.18: Explain why the function is discontinuous at the given number . Ske...
 2.4.19: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.4.20: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.4.21: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.4.22: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.4.23: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.4.24: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.4.25: Locate the discontinuities of the function and illustrate by graphing.
 2.4.26: Locate the discontinuities of the function and illustrate by graphing.
 2.4.27: Use continuity to evaluate the limit.
 2.4.28: Use continuity to evaluate the limit.
 2.4.29: Use continuity to evaluate the limit.
 2.4.30: Use continuity to evaluate the limit.
 2.4.31: Show that is continuous on .fx x2 if x 1 sx if x 1
 2.4.32: Show that is continuous on .fx sin x if x 4cos x if x 4
 2.4.33: Find the numbers at which the functionfx x 2 ex 2 xif x 0 if 0x1 if...
 2.4.34: The gravitational force exerted by the earth on a unit mass at a di...
 2.4.35: For what value of the constant is the function continuous on ?fx cx...
 2.4.36: Find the values of and that make continuous everywhere.fx x2 4 x 2 ...
 2.4.37: Which of the following functions has a removable discontinuity at ?...
 2.4.38: Suppose that a function is continuous on [0, 1] except at 0.25 and ...
 2.4.39: If , show that there is a number such that .
 2.4.40: Suppose is continuous on and the only solutions of the equation are...
 2.4.41: Use the Intermediate Value Theorem to show that there is a root of ...
 2.4.42: Use the Intermediate Value Theorem to show that there is a root of ...
 2.4.43: Use the Intermediate Value Theorem to show that there is a root of ...
 2.4.44: Use the Intermediate Value Theorem to show that there is a root of ...
 2.4.45: (a) Prove that the equation has at least one real root. (b) Use you...
 2.4.46: (a) Prove that the equation has at least one real root. (b) Use you...
 2.4.47: (a) Prove that the equation has at least one real root. (b) Use you...
 2.4.48: (a) Prove that the equation has at least one real root. (b) Use you...
 2.4.49: To prove that sine is continuous we need to show that for every rea...
 2.4.50: Prove that cosine is a continuous function.
 2.4.51: Is there a number that is exactly 1 more than its cube?
 2.4.52: If and are positive numbers, prove that the equation a x3 2x2 1b x3...
 2.4.53: Show that the function fx x4 sin1x 0if x 0 if x 0 is continuous on
 2.4.54: (a) Show that the absolute value function is continuous everywhere....
 2.4.55: A Tibetan monk leaves the monastery at 7:00 AM and takes his usual ...
Solutions for Chapter 2.4: CONTINUITY
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series)  4th Edition
ISBN: 9780495559726
Solutions for Chapter 2.4: CONTINUITY
Get Full SolutionsChapter 2.4: CONTINUITY includes 55 full stepbystep solutions. Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) was written by and is associated to the ISBN: 9780495559726. This textbook survival guide was created for the textbook: Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series), edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Since 55 problems in chapter 2.4: CONTINUITY have been answered, more than 21095 students have viewed full stepbystep solutions from this chapter.

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

Complex fraction
See Compound fraction.

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Continuous function
A function that is continuous on its entire domain

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Geometric series
A series whose terms form a geometric sequence.

Graphical model
A visible representation of a numerical or algebraic model.

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Imaginary unit
The complex number.

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Linear regression
A procedure for finding the straight line that is the best fit for the data

Nappe
See Right circular cone.

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Slopeintercept form (of a line)
y = mx + b

Time plot
A line graph in which time is measured on the horizontal axis.

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.