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
Evaluate the limit and justify each step by indicating the appropriate Limit Theorem(s) used in each step which is the 2nd picture attatched. thank you
![REMEMBER!
THEOREMS ON LIMITS
THEOREM 1: The limit of the sum of two (or more) functions is equal to the sum of
their limits
nd for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmittin in any form or by
ronic, mechanical, photocopying, recording, or ofherwise of any part of this document, without the prior written permission of SLU, is strictiy prohibite
lim[u(x) + v(x)] = lim u(x) + lim v(x)
THEOREM 2: The limit of the product of two (or more) functions is equal to the product of
their limits
lim[u(x)v(x)] = [im u(x] [im v(x)]
THEOREM 3: The limit of the quotient of two functions is equal to the quotient of their limits
provided the limit of the denominator is not zero
lim u(x)]
lim v(x)
[u(x)]
lim
if Him v(x)] # 0
Lx-a
x-a v(x)
Lx-a
Lx-a
THEOREM 4: If a is measured in radians, lim
sinoc
= 1
THEOREM 5: The limit of a constant is the constant itself
lim k = k where k is any constant
THEOREM 6: The limit of a constant times a function is the constant times the limit of the
function.
lim[ku(x)] = k lim u(x) where k is any constant
SITY](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2860ef0d-33ac-4504-8382-2fc2e2a614d3%2Fad4b1377-aca5-4757-a915-f7310c2cf5be%2F0f6mtwu_processed.png&w=3840&q=75)
Transcribed Image Text:REMEMBER!
THEOREMS ON LIMITS
THEOREM 1: The limit of the sum of two (or more) functions is equal to the sum of
their limits
nd for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmittin in any form or by
ronic, mechanical, photocopying, recording, or ofherwise of any part of this document, without the prior written permission of SLU, is strictiy prohibite
lim[u(x) + v(x)] = lim u(x) + lim v(x)
THEOREM 2: The limit of the product of two (or more) functions is equal to the product of
their limits
lim[u(x)v(x)] = [im u(x] [im v(x)]
THEOREM 3: The limit of the quotient of two functions is equal to the quotient of their limits
provided the limit of the denominator is not zero
lim u(x)]
lim v(x)
[u(x)]
lim
if Him v(x)] # 0
Lx-a
x-a v(x)
Lx-a
Lx-a
THEOREM 4: If a is measured in radians, lim
sinoc
= 1
THEOREM 5: The limit of a constant is the constant itself
lim k = k where k is any constant
THEOREM 6: The limit of a constant times a function is the constant times the limit of the
function.
lim[ku(x)] = k lim u(x) where k is any constant
SITY
Transcribed Image Text:PIENTIA
(a)
lim (3xª + 2x² - x + 1)
X-2
EDIFICA
1 + 3x
lim
1 + 4x? + 3x*
(b)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 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