Answered: z² + 4z + 4 f(2) = - 4z +4 f(2) =미 lim… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 8E

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Question

p(x)
Suppose that p(x) and q(x) are polynomials. The expression lim
I-a g(1)
P(z)
= L means that as a gets very close to a -- without being a, the output
q(z)
gets very close to L. How to find L?
• If q(a) + 0, then L =
p(a)
That's simply the evaluation of the function at a.
q(a)
• If p(a) = 0 and g(a) = 0, then p(x) and g(z) have a common factor. Factor both polynomials and cancel the common factors out. Then L is the limit of the equivalent function.
• If p(a) + 0 and g(a) = 0, find the one-sided limits and compare them.
Practice
2² + 4x + 4
1.
f(x) =
f(2) =
lim
2² – 4r + 4
f(z) =
x² + 2x
72 - 27
lim f(x) =
2.
f(x) =
f(2) =
I-2
1² + 4x + 4
3.
f(x) =
f(2) =
lim
12 – 4
(x) =/
72
f(x) =
4x + 4
f(2) =
lim f(æ)
4.
=
x² – 4
x? – 4
5.
f(x) =
12 – 2x
f(2)
lim f(x) =

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