 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 726, find the limit (if it exists). If it does not exi...
 1.4.8: In Exercises 726, find the limit (if it exists). If it does not exi...
 1.4.9: In Exercises 726, find the limit (if it exists). If it does not exi...
 1.4.10: lim x2 2 x x2 4 l
 1.4.11: lim x3 x x2 9 li
 1.4.12: lim x9 x 3 x 9 lim
 1.4.13: lim x0 x x
 1.4.14: lim x10 x 10 x 10 l
 1.4.15: lim x0 1 x x 1 x x l
 1.4.16: lim x0 x x2 x x x2 x x
 1.4.17: In Exercises 726, find the limit (if it exists). If it does not exi...
 1.4.18: In Exercises 726, find the limit (if it exists). If it does not exi...
 1.4.19: In Exercises 726, find the limit (if it exists). If it does not exi...
 1.4.20: In Exercises 726, find the limit (if it exists). If it does not exi...
 1.4.21: lim x cot x
 1.4.22: lim x 2 sec x
 1.4.23: lim x4 5x 7 l
 1.4.24: lim x2 2x x
 1.4.25: lim x3 2 x l
 1.4.26: lim x1 1 x 2 l
 1.4.27: In Exercises 2730, discuss the continuity of each function.fx 1 x2 4 l
 1.4.28: In Exercises 2730, discuss the continuity of each function.fx x2 1 ...
 1.4.29: In Exercises 2730, discuss the continuity of each function.fx 1 2x x
 1.4.30: In Exercises 2730, discuss the continuity of each function.fx x, 2,...
 1.4.31: In Exercises 3134, discuss the continuity of the function on the cl...
 1.4.32: In Exercises 3134, discuss the continuity of the function on the cl...
 1.4.33: In Exercises 3134, discuss the continuity of the function on the cl...
 1.4.34: In Exercises 3134, discuss the continuity of the function on the cl...
 1.4.35: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.36: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.37: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.38: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.39: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.40: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.41: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.42: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.43: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.44: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.45: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.46: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.47: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.48: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.49: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.50: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.51: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.52: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.53: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.54: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.55: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.56: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.57: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.58: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.59: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.60: In Exercises 35 60, find the values (if any) at which is not conti...
 1.4.61: In Exercises 61 and 62, use a graphing utility to graph the functio...
 1.4.62: In Exercises 61 and 62, use a graphing utility to graph the functio...
 1.4.63: fx 3x2, ax 4, x 1 x < 1 b
 1.4.64: fx 3x3 , ax 5, x 1 x > 1 f
 1.4.65: fx x3 , ax2 , x 2 x > 2
 1.4.66: gx 4 sin x x , x < 0 a 2x, x 0 f
 1.4.67: fx 2, ax b, 2, x 1 1 < x < 3 x 3 gx
 1.4.68: gx x2 a2 x a , x a 8, x a fx
 1.4.69: In Exercises 69 72, discuss the continuity of the composite functio...
 1.4.70: In Exercises 69 72, discuss the continuity of the composite functio...
 1.4.71: In Exercises 69 72, discuss the continuity of the composite functio...
 1.4.72: In Exercises 69 72, discuss the continuity of the composite functio...
 1.4.73: fx x x x
 1.4.74: hx 1 x2 x 2 fx
 1.4.75: gx x2 3x, 2x 5, x > 4 x 4 h
 1.4.76: fx cos x 1 x , x < 0 5x, x 0 g
 1.4.77: In Exercises 77 80, describe the interval(s) on which the function ...
 1.4.78: In Exercises 77 80, describe the interval(s) on which the function ...
 1.4.79: In Exercises 77 80, describe the interval(s) on which the function ...
 1.4.80: In Exercises 77 80, describe the interval(s) on which the function ...
 1.4.81: In Exercises 81 and 82, use a graphing utility to graph the functio...
 1.4.82: In Exercises 81 and 82, use a graphing utility to graph the functio...
 1.4.83: In Exercises 8386, explain why the function has a zero in the given...
 1.4.84: In Exercises 8386, explain why the function has a zero in the given...
 1.4.85: In Exercises 8386, explain why the function has a zero in the given...
 1.4.86: In Exercises 8386, explain why the function has a zero in the given...
 1.4.87: In Exercises 8790, use the Intermediate Value Theorem and a graphin...
 1.4.88: In Exercises 8790, use the Intermediate Value Theorem and a graphin...
 1.4.89: In Exercises 8790, use the Intermediate Value Theorem and a graphin...
 1.4.90: In Exercises 8790, use the Intermediate Value Theorem and a graphin...
 1.4.91: In Exercises 9194, verify that the Intermediate Value Theorem appli...
 1.4.92: In Exercises 9194, verify that the Intermediate Value Theorem appli...
 1.4.93: In Exercises 9194, verify that the Intermediate Value Theorem appli...
 1.4.94: In Exercises 9194, verify that the Intermediate Value Theorem appli...
 1.4.95: State how continuity is destroyed at for each of the following grap...
 1.4.96: Sketch the graph of any function such that and Is the function cont...
 1.4.97: If the functions and are continuous for all real is always continuo...
 1.4.98: Describe the difference between a discontinuity that is removable a...
 1.4.99: In Exercises 99102, determine whether the statement is true or fals...
 1.4.100: In Exercises 99102, determine whether the statement is true or fals...
 1.4.101: In Exercises 99102, determine whether the statement is true or fals...
 1.4.102: In Exercises 99102, determine whether the statement is true or fals...
 1.4.103: Every day you dissolve 28 ounces of chlorine in a swimming pool. Th...
 1.4.104: Describe how the functions and differ.
 1.4.105: A long distance phone service charges $0.40 for the first 10 minute...
 1.4.106: The number of units in inventory in a small company is given by whe...
 1.4.107: At 8:00 A.M. on Saturday a man begins running up the side of a moun...
 1.4.108: Use the Intermediate Value Theorem to show that for all spheres wit...
 1.4.109: Prove that if is continuous and has no zeros on then either fx > 0 ...
 1.4.110: Show that the Dirichlet function is not continuous at any real number.
 1.4.111: Show that the function is continuous only at (Assume that is any no...
 1.4.112: The signum function is defined by Sketch a graph of sgn and find th...
 1.4.113: The table lists the speeds (in feet per second) of a falling object...
 1.4.114: A swimmer crosses a pool of width by swimming in a straight line fr...
 1.4.115: Find all values of such that is continuous on fx 1 x2, x, x c x > c c
 1.4.116: Prove that for any real number there exists i
 1.4.117: Let What is the domain of How can you define at in order for to be ...
 1.4.118: Prove that if then is continuous at c
 1.4.119: Discuss the continuity of the function hx xx.
 1.4.120: (a) Let and be continuous on the closed interval If and prove that ...
 1.4.121: Prove or disprove: if and are real numbers with and then
 1.4.122: Determine all polynomials such that and These problems were compose...
Solutions for Chapter 1.4: Continuity and OneSided Limits
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 1.4: Continuity and OneSided Limits
Get Full SolutionsChapter 1.4: Continuity and OneSided Limits includes 122 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9. Since 122 problems in chapter 1.4: Continuity and OneSided Limits have been answered, more than 63212 students have viewed full stepbystep solutions from this chapter. Calculus was written by and is associated to the ISBN: 9780547167022.

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

Directed line segment
See Arrow.

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

Doubleangle identity
An identity involving a trigonometric function of 2u

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.

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Leading term
See Polynomial function in x.

Length of an arrow
See Magnitude of an arrow.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Logistic regression
A procedure for fitting a logistic curve to a set of data

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Scalar
A real number.

Second
Angle measure equal to 1/60 of a minute.

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Solve by elimination or substitution
Methods for solving systems of linear equations.

Third quartile
See Quartile.