 1.4.1: In Exercises 16, use the graph to determine the limit, and discuss ...
 1.4.2: In Exercises 16, use the graph to determine the limit, and discuss ...
 1.4.3: In Exercises 16, use the graph to determine the limit, and discuss ...
 1.4.4: In Exercises 16, use the graph to determine the limit, and discuss ...
 1.4.5: In Exercises 16, use the graph to determine the limit, and discuss ...
 1.4.6: In Exercises 16, use the graph to determine the limit, and discuss ...
 1.4.7: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.8: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.9: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.10: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.11: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.12: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.13: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.14: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.15: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.16: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.17: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.18: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.19: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.20: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.21: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.22: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.23: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.24: In Exercises 724, find the limit (if it exists). If it does not exi...
 1.4.25: In Exercises 2528, discuss the continuity of each function. y9
 1.4.26: In Exercises 2528, discuss the continuity of each function. 9x
 1.4.27: In Exercises 2528, discuss the continuity of each function. 9x2
 1.4.28: In Exercises 2528, discuss the continuity of each function. 9x2y
 1.4.29: In Exercises 2932, discuss the continuity of the function on the cl...
 1.4.30: In Exercises 2932, discuss the continuity of the function on the cl...
 1.4.31: In Exercises 2932, discuss the continuity of the function on the cl...
 1.4.32: In Exercises 2932, discuss the continuity of the function on the cl...
 1.4.33: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.34: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.35: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.36: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.37: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.38: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.39: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.40: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.41: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.42: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.43: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.44: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.45: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.46: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.47: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.48: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.49: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.50: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.51: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.52: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.53: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.54: In Exercises 3354, find the values (if any) at which is not contin...
 1.4.55: In Exercises 55 and 56, use a graphing utility to graph the functio...
 1.4.56: In Exercises 55 and 56, use a graphing utility to graph the functio...
 1.4.57: In Exercises 5760, find the constant or the constants and such that...
 1.4.58: In Exercises 5760, find the constant or the constants and such that...
 1.4.59: In Exercises 5760, find the constant or the constants and such that...
 1.4.60: In Exercises 5760, find the constant or the constants and such that...
 1.4.61: In Exercises 61 64, discuss the continuity of the composite functio...
 1.4.62: In Exercises 61 64, discuss the continuity of the composite functio...
 1.4.63: In Exercises 61 64, discuss the continuity of the composite functio...
 1.4.64: In Exercises 61 64, discuss the continuity of the composite functio...
 1.4.65: In Exercises 6568, use a graphing utility to graph the function. Us...
 1.4.66: In Exercises 6568, use a graphing utility to graph the function. Us...
 1.4.67: In Exercises 6568, use a graphing utility to graph the function. Us...
 1.4.68: In Exercises 6568, use a graphing utility to graph the function. Us...
 1.4.69: In Exercises 6972, describe the interval(s) on which the function i...
 1.4.70: In Exercises 6972, describe the interval(s) on which the function i...
 1.4.71: In Exercises 6972, describe the interval(s) on which the function i...
 1.4.72: In Exercises 6972, describe the interval(s) on which the function i...
 1.4.73: Writing In Exercises 73 and 74, use a graphing utility to graph the...
 1.4.74: Writing In Exercises 73 and 74, use a graphing utility to graph the...
 1.4.75: Writing In Exercises 7578, explain why the function has a zero in t...
 1.4.76: Writing In Exercises 7578, explain why the function has a zero in t...
 1.4.77: Writing In Exercises 7578, explain why the function has a zero in t...
 1.4.78: Writing In Exercises 7578, explain why the function has a zero in t...
 1.4.79: In Exercises 7982, use the Intermediate Value Theorem and a graphin...
 1.4.80: In Exercises 7982, use the Intermediate Value Theorem and a graphin...
 1.4.81: In Exercises 7982, use the Intermediate Value Theorem and a graphin...
 1.4.82: In Exercises 7982, use the Intermediate Value Theorem and a graphin...
 1.4.83: In Exercises 8386, verify that the Intermediate Value Theorem appli...
 1.4.84: In Exercises 8386, verify that the Intermediate Value Theorem appli...
 1.4.85: In Exercises 8386, verify that the Intermediate Value Theorem appli...
 1.4.86: In Exercises 8386, verify that the Intermediate Value Theorem appli...
 1.4.87: State how continuity is destroyed at for each of the following grap...
 1.4.88: Describe the difference between a discontinuity that is removable a...
 1.4.89: Sketch the graph of any function such that and x2y
 1.4.90: If the functions and are continuous for all real is always continuo...
 1.4.91: True or False? In Exercises 9194, determine whether the statement i...
 1.4.92: True or False? In Exercises 9194, determine whether the statement i...
 1.4.93: True or False? In Exercises 9194, determine whether the statement i...
 1.4.94: True or False? In Exercises 9194, determine whether the statement i...
 1.4.95: Swimming Pool Every day you dissolve 28 ounces of chlorine in a swi...
 1.4.96: Think About It Describe how the functions and differ 4xy
 1.4.97: Telephone Charges A dialdirect long distance call between two citi...
 1.4.98: Inventory Management The number of units in inventory in a small co...
 1.4.99: Dj Vu At 8:00 A.M. on Saturday a man begins running up the side of ...
 1.4.100: Volume Use the Intermediate Value Theorem to show that for all sphe...
 1.4.101: Prove that if is continuous and has no zeros on then either for all...
 1.4.102: Show that the Dirichlet function is not continuous at any real numb...
 1.4.103: Show that the function is continuous only at (Assume that is any no...
 1.4.104: The signum function is defined by Sketch a graph of sgn and find th...
 1.4.105: Modeling Data After an object falls for seconds, the speed (in feet...
 1.4.106: Creating Models A swimmer crosses a pool of width by swimming in a ...
 1.4.107: Find all values of such that is continuous on 2x2x
 1.4.108: Prove that for any real number there exists in such that x2xy
 1.4.109: Let What is the domain of How can you define at in order for to be ...
 1.4.110: Prove that if then is continuous at xy
 1.4.111: Discuss the continuity of the function xyx
 1.4.112: (a) Let and be continuous on the closed interval If and prove that ...
 1.4.113: Prove or disprove: if and are real numbers with and then x3
 1.4.114: Determine all polynomials such that and x3
Solutions for Chapter 1.4: Continuity and OneSided Limits
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 1.4: Continuity and OneSided Limits
Get Full SolutionsSince 114 problems in chapter 1.4: Continuity and OneSided Limits have been answered, more than 78358 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.4: Continuity and OneSided Limits includes 114 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780618502981. This textbook survival guide was created for the textbook: Calculus, edition: 8.

Amplitude
See Sinusoid.

Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Circle
A set of points in a plane equally distant from a fixed point called the center

Cube root
nth root, where n = 3 (see Principal nth root),

Differentiable at x = a
ƒ'(a) exists

Directed distance
See Polar coordinates.

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Endpoint of an interval
A real number that represents one “end” of an interval.

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

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

Inequality symbol or
<,>,<,>.

Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers

Pie chart
See Circle graph.

Solve by substitution
Method for solving systems of linear equations.

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

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.