Example. (example 3) Since lim In(z) = In(1) = 0, we can say that the funetion f(z) = In(z) is continuous at z = 1. Problem. (problem 3) Since lim tan (z) = tan¯(v3) = x/3, we can say that the function f(z) = is continuous at z = If a function is continuous at each point in an interval, I, then we say that f(z) is continuous on I. A function f(z) is called continuous from the left at z = a if lim f(z) = f(a), and it is called continuous from the right at z = a if lim f(z) = f(a). Note that if f(z) is continuous at z = a then it is both continuous from the left and continuous from the right at z = a. If for some reason, a limit cannot be computed by plugging in, then we say that the function is discontinuous. In other words, if lim f(z) + f(a),
Example. (example 3) Since lim In(z) = In(1) = 0, we can say that the funetion f(z) = In(z) is continuous at z = 1. Problem. (problem 3) Since lim tan (z) = tan¯(v3) = x/3, we can say that the function f(z) = is continuous at z = If a function is continuous at each point in an interval, I, then we say that f(z) is continuous on I. A function f(z) is called continuous from the left at z = a if lim f(z) = f(a), and it is called continuous from the right at z = a if lim f(z) = f(a). Note that if f(z) is continuous at z = a then it is both continuous from the left and continuous from the right at z = a. If for some reason, a limit cannot be computed by plugging in, then we say that the function is discontinuous. In other words, if lim f(z) + f(a),
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
number 3 is a little tougher than i thought it would be

Transcribed Image Text:O Ma
6 Sch
6 You
E Unt
E Eng
E Unt
E Ho X x
Б Ans
NFL Gar
ESC
Cha
M Inb
cA Rol
G 2-S
Inb
G Col
n Gra
R Gra
O Atla
G for
а Am
+
i ximera.osu.edu/math/calc1Book/calcBook/continuity/continuity
E Apps
e 8 Puerto Rican Dish..
arizona waterparks
arkansas waterparks
E Reading list
XIMERA
O Get Help
* Math Editor
A Save
Erase
-) Sign In -
Example. (example 3) Since
lim In(x) = In(1) = 0,
we can say that the function f(x) = In(x) is continuous at x = 1.
Problem. (problem 3) Since
lim_tan
(x)
= tan(V3)
= T/3,
we can say that the function f(x)
? is continuous at a =
?
If a function is continuous at each point in an interval, I, then we say that f(x) is continuous on I.
A function f(x) is called continuous from the left at x = a if
lim f(x) = f(a),
and it is called continuous from the right at a = a if
lim f(x) = f(a).
Note that if f(x) is continuous at x = a then it is both continuous from the left and continuous from the right at x = a.
If for some reason, a limit cannot be computed by plugging in, then we say that the function is discontinuous. In other words, if
lim f(x) + f(a),
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images

Recommended textbooks for you

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning