Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 12E
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
![PIENTIA
(a)
lim (3xª + 2x² - x + 1)
X-2
EDIFICA
1 + 3x
lim
1 + 4x? + 3x*
(b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2860ef0d-33ac-4504-8382-2fc2e2a614d3%2Fad4b1377-aca5-4757-a915-f7310c2cf5be%2Fy9jond_processed.png&w=3840&q=75)
Transcribed Image Text:PIENTIA
(a)
lim (3xª + 2x² - x + 1)
X-2
EDIFICA
1 + 3x
lim
1 + 4x? + 3x*
(b)
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