 2.5.1: Write an equation that expresses the fact that a function f is cont...
 2.5.2: . If f is continuous on s2`, `d, what can you say about its graph?
 2.5.3: (a) From the graph of f, state the numbers at which f is discontinu...
 2.5.4: From the graph of t, state the intervals on which t is continuous.
 2.5.5: Sketch the graph of a function f that is continuous except for the ...
 2.5.6: Sketch the graph of a function f that is continuous except for the ...
 2.5.7: Sketch the graph of a function f that is continuous except for the ...
 2.5.8: Sketch the graph of a function f that is continuous except for the ...
 2.5.9: The toll T charged for driving on a certain stretch of a toll road ...
 2.5.10: Explain why each function is continuous or discontinuous. (a) The t...
 2.5.11: Use the definition of continuity and the properties of limits to sh...
 2.5.12: Use the definition of continuity and the properties of limits to sh...
 2.5.13: Use the definition of continuity and the properties of limits to sh...
 2.5.14: Use the definition of continuity and the properties of limits to sh...
 2.5.15: Use the definition of continuity and the properties of limits to sh...
 2.5.16: Use the definition of continuity and the properties of limits to sh...
 2.5.17: Explain why the function is discontinuous at the given number a. Sk...
 2.5.18: Explain why the function is discontinuous at the given number a. Sk...
 2.5.19: Explain why the function is discontinuous at the given number a. Sk...
 2.5.20: Explain why the function is discontinuous at the given number a. Sk...
 2.5.21: Explain why the function is discontinuous at the given number a. Sk...
 2.5.22: Explain why the function is discontinuous at the given number a. Sk...
 2.5.23: How would you remove the discontinuity of f ? In other words, how w...
 2.5.24: How would you remove the discontinuity of f ? In other words, how w...
 2.5.25: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.26: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.27: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.28: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.29: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.30: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.31: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.32: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.5.33: Locate the discontinuities of the function and illustrate by graphi...
 2.5.34: Locate the discontinuities of the function and illustrate by graphi...
 2.5.35: Use continuity to evaluate the limit. lim xl2 x s20 2 x 2
 2.5.36: Use continuity to evaluate the limit. lim xl sinsx 1 sin xd
 2.5.37: Use continuity to evaluate the limit. lim xl1 lnS 5 2 x 2 1 1 x D
 2.5.38: Use continuity to evaluate the limit. lim xl4 3sx 222x24
 2.5.39: Show that f is continuous on s2`, `d. fsxd H 1 2 x 2 if x < 1 lnx i...
 2.5.40: Show that f is continuous on s2`, `d. fsxd H sin x if x , y4 cos x ...
 2.5.41: Find the numbers at which f is discontinuous. At which of these num...
 2.5.42: Find the numbers at which f is discontinuous. At which of these num...
 2.5.43: Find the numbers at which f is discontinuous. At which of these num...
 2.5.44: The gravitational force exerted by the planet Earth on a unit mass ...
 2.5.45: For what value of the constant c is the function f continuous on s2...
 2.5.46: Find the values of a and b that make f continuous everywhere. fsxd ...
 2.5.47: Suppose f and t are continuous functions such that ts2d 6 and limx ...
 2.5.48: Let fsxd 1yx and tsxd 1yx 2 . (a) Find s f + tds xd. (b) Is f + t c...
 2.5.49: Which of the following functions f has a removable discontinuity at...
 2.5.50: Suppose that a function f is continuous on [0, 1] except at 0.25 an...
 2.5.51: If fsxd x 2 1 10 sin x, show that there is a number c such that fsc...
 2.5.52: Suppose f is continuous on f1, 5g and the only solutions of the equ...
 2.5.53: Use the Intermediate Value Theorem to show that there is a root of ...
 2.5.54: Use the Intermediate Value Theorem to show that there is a root of ...
 2.5.55: Use the Intermediate Value Theorem to show that there is a root of ...
 2.5.56: Use the Intermediate Value Theorem to show that there is a root of ...
 2.5.57: 8 (a) Prove that the equation has at least one real root. (b) Use y...
 2.5.58: 8 (a) Prove that the equation has at least one real root. (b) Use y...
 2.5.59: (a) Prove that the equation has at least one real root. (b) Use you...
 2.5.60: (a) Prove that the equation has at least one real root. (b) Use you...
 2.5.61: Prove, without graphing, that the graph of the function has at leas...
 2.5.62: Prove, without graphing, that the graph of the function has at leas...
 2.5.63: Prove that f is continuous at a if and only if lim h l0 fsa 1 hd fsa
 2.5.64: To prove that sine is continuous, we need to show that limx l a sin...
 2.5.65: Prove that cosine is a continuous function.
 2.5.66: (a) Prove Theorem 4, part 3. (b) Prove Theorem 4, part 5.
 2.5.67: For what values of x is f continuous? fsxd H 0 1 if x is rational i...
 2.5.68: For what values of x is t continuous? tsxd H 0 x if x is rational i...
 2.5.69: Is there a number t hat is exactly 1 more than its cube?
 2.5.70: Is there a number t hat is exactly 1 more than its cube?
 2.5.71: Show that the function fsxd H x 4 sins1yxd 0 if x 0 if x 0 is conti...
 2.5.72: (a) Show that the absolute value function Fsxd  x  is continuous ...
 2.5.73: A Tibetan monk leaves the monastery at 7:00 am and takes his usual ...
Solutions for Chapter 2.5: Continuity
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 2.5: Continuity
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.5: Continuity includes 73 full stepbystep solutions. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Since 73 problems in chapter 2.5: Continuity have been answered, more than 38035 students have viewed full stepbystep solutions from this chapter.

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Common difference
See Arithmetic sequence.

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Constant term
See Polynomial function

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

Pointslope form (of a line)
y  y1 = m1x  x 12.

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)

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Quotient polynomial
See Division algorithm for polynomials.

Unit circle
A circle with radius 1 centered at the origin.

Unit vector
Vector of length 1.

Vertex of an angle
See Angle.

yzplane
The points (0, y, z) in Cartesian space.

Zero vector
The vector <0,0> or <0,0,0>.