 2.6.1: Which of the following functions are continuous for all values in t...
 2.6.2: Give the three conditions that must be satisfied by a function to b...
 2.6.3: What does it mean for a function to be continuous on an interval?
 2.6.4: We informally describe a function f to be continuous at a if its gr...
 2.6.5: Complete the following sentences. a. A function is continuous from ...
 2.6.6: Describe the points (if any) at which a rational function fails to ...
 2.6.7: What is the domain of f 1x2 = ex>x and where is f continuous?
 2.6.8: Explain the Intermediate Value Theorem using words and pictures.
 2.6.9: 912. Discontinuities from a graph Determine the points at which the...
 2.6.10: 912. Discontinuities from a graph Determine the points at which the...
 2.6.11: 912. Discontinuities from a graph Determine the points at which the...
 2.6.12: 912. Discontinuities from a graph Determine the points at which the...
 2.6.13: 1320. Continuity at a point Determine whether the following functio...
 2.6.14: 1320. Continuity at a point Determine whether the following functio...
 2.6.15: 1320. Continuity at a point Determine whether the following functio...
 2.6.16: 1320. Continuity at a point Determine whether the following functio...
 2.6.17: 1320. Continuity at a point Determine whether the following functio...
 2.6.18: 1320. Continuity at a point Determine whether the following functio...
 2.6.19: 1320. Continuity at a point Determine whether the following functio...
 2.6.20: 1320. Continuity at a point Determine whether the following functio...
 2.6.21: 2126. Continuity on intervals Use Theorem 2.10 to determine the int...
 2.6.22: 2126. Continuity on intervals Use Theorem 2.10 to determine the int...
 2.6.23: 2126. Continuity on intervals Use Theorem 2.10 to determine the int...
 2.6.24: 2126. Continuity on intervals Use Theorem 2.10 to determine the int...
 2.6.25: 2126. Continuity on intervals Use Theorem 2.10 to determine the int...
 2.6.26: 2126. Continuity on intervals Use Theorem 2.10 to determine the int...
 2.6.27: 2730. Limits of compositions Evaluate each limit and justify your a...
 2.6.28: 2730. Limits of compositions Evaluate each limit and justify your a...
 2.6.29: 2730. Limits of compositions Evaluate each limit and justify your a...
 2.6.30: 2730. Limits of compositions Evaluate each limit and justify your a...
 2.6.31: 3134. Limits of composite functions Evaluate each limit and justify...
 2.6.32: 3134. Limits of composite functions Evaluate each limit and justify...
 2.6.33: 3134. Limits of composite functions Evaluate each limit and justify...
 2.6.34: 3134. Limits of composite functions Evaluate each limit and justify...
 2.6.35: 3538. Intervals of continuity Determine the intervals of continuity...
 2.6.36: 3538. Intervals of continuity Determine the intervals of continuity...
 2.6.37: 3538. Intervals of continuity Determine the intervals of continuity...
 2.6.38: 3538. Intervals of continuity Determine the intervals of continuity...
 2.6.39: Intervals of continuity Let f 1x2 = e 2x if x 6 1 x2 + 3x if x 1. a...
 2.6.40: Intervals of continuity Let f 1x2 = e x3 + 4x + 1 if x 0 2x3 if x 7...
 2.6.41: 4146. Functions with roots Determine the interval(s) on which the f...
 2.6.42: 4146. Functions with roots Determine the interval(s) on which the f...
 2.6.43: 4146. Functions with roots Determine the interval(s) on which the f...
 2.6.44: 4146. Functions with roots Determine the interval(s) on which the f...
 2.6.45: 4146. Functions with roots Determine the interval(s) on which the f...
 2.6.46: 4146. Functions with roots Determine the interval(s) on which the f...
 2.6.47: 4750. Limits with roots Evaluate each limit and justify your answer...
 2.6.48: 4750. Limits with roots Evaluate each limit and justify your answer...
 2.6.49: 4750. Limits with roots Evaluate each limit and justify your answer...
 2.6.50: 4750. Limits with roots Evaluate each limit and justify your answer...
 2.6.51: 5156. Continuity and limits with transcendental functions Determine...
 2.6.52: 5156. Continuity and limits with transcendental functions Determine...
 2.6.53: 5156. Continuity and limits with transcendental functions Determine...
 2.6.54: 5156. Continuity and limits with transcendental functions Determine...
 2.6.55: 5156. Continuity and limits with transcendental functions Determine...
 2.6.56: 5156. Continuity and limits with transcendental functions Determine...
 2.6.57: Intermediate Value Theorem and interest rates Suppose $5000 is inve...
 2.6.58: Intermediate Value Theorem and mortgage payments You are shopping f...
 2.6.59: 5964. Applying the Intermediate Value Theorem a. Use the Intermedia...
 2.6.60: 5964. Applying the Intermediate Value Theorem a. Use the Intermedia...
 2.6.61: 5964. Applying the Intermediate Value Theorem a. Use the Intermedia...
 2.6.62: 5964. Applying the Intermediate Value Theorem a. Use the Intermedia...
 2.6.63: 5964. Applying the Intermediate Value Theorem a. Use the Intermedia...
 2.6.64: 5964. Applying the Intermediate Value Theorem a. Use the Intermedia...
 2.6.65: Explain why or why not Determine whether the following statements a...
 2.6.66: Continuity of the absolute value function Prove that the absolute v...
 2.6.67: 6770. Continuity of functions with absolute values Use the continui...
 2.6.68: 6770. Continuity of functions with absolute values Use the continui...
 2.6.69: 6770. Continuity of functions with absolute values Use the continui...
 2.6.70: 6770. Continuity of functions with absolute values Use the continui...
 2.6.71: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.72: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.73: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.74: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.75: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.76: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.77: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.78: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.79: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.80: 7180. Miscellaneous limits Evaluate the following limits or state t...
 2.6.81: Pitfalls using technology The graph of the sawtooth function y = x ...
 2.6.82: Pitfalls using technology Graph the function f 1x2 = sin x x using ...
 2.6.83: Sketching functions a. Sketch the graph of a function that is not c...
 2.6.84: An unknown constant Determine the value of the constant a for which...
 2.6.85: An unknown constant Let g1x2 = x2 + x if x 6 1 a if x = 1 3x + 5 if...
 2.6.86: Asymptotes of a function containing exponentials Let f 1x2 = 2ex + ...
 2.6.87: Asymptotes of a function containing exponentials Let f 1x2 = 2ex + ...
 2.6.88: 8889. Applying the Intermediate Value Theorem Use the Intermediate ...
 2.6.89: 8889. Applying the Intermediate Value Theorem Use the Intermediate ...
 2.6.90: Parking costs Determine the intervals of continuity for the parking...
 2.6.91: Investment problem Assume you invest $250 at the end of each year f...
 2.6.92: Applying the Intermediate Value Theorem Suppose you park your car a...
 2.6.93: The monk and the mountain A monk set out from a monastery in the va...
 2.6.94: Does continuity of _ f _ imply continuity of f ? Let g1x2 = e 1 if ...
 2.6.95: 9596. Classifying discontinuities The discontinuities in graphs (a)...
 2.6.96: 9596. Classifying discontinuities The discontinuities in graphs (a)...
 2.6.97: 9798. Removable discontinuities Show that the following functions h...
 2.6.98: 9798. Removable discontinuities Show that the following functions h...
 2.6.99: Do removable discontinuities exist? See Exercises 9596. a. Does the...
 2.6.100: 100101. Classifying discontinuities Classify the discontinuities in...
 2.6.101: 100101. Classifying discontinuities Classify the discontinuities in...
 2.6.102: Continuity of composite functions Prove Theorem 2.11: If g is conti...
 2.6.103: Continuity of compositions a. Find functions f and g such that each...
 2.6.104: Violation of the Intermediate Value Theorem? Let f 1x2 = _ x _ x . ...
 2.6.105: Continuity of sin x and cos x a. Use the identity sin 1a + h2 = sin...
Solutions for Chapter 2.6: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 2.6
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.6 includes 105 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Since 105 problems in chapter 2.6 have been answered, more than 56676 students have viewed full stepbystep solutions from this chapter.

Amplitude
See Sinusoid.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Cone
See Right circular cone.

Continuous function
A function that is continuous on its entire domain

Course
See Bearing.

Direction of an arrow
The angle the arrow makes with the positive xaxis

Halfangle identity
Identity involving a trigonometric function of u/2.

Identity properties
a + 0 = a, a ? 1 = a

kth term of a sequence
The kth expression in the sequence

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Multiplication principle of counting
A principle used to find the number of ways an event can occur.

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Orthogonal vectors
Two vectors u and v with u x v = 0.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Positive angle
Angle generated by a counterclockwise rotation.

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

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j