B. 1. f(-4) 2. lim f(x) X--3+ 3. lim f(x) x-0 4. lim f(x) 5. lim f(x) x-5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![B.
V V
1. f(-4)
2. lim f(x)
3. lim f(x)
4. lim f(x)
5. lim f(x)
x-5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b193593-6dda-4d9a-96a1-bcbfa3928dc6%2F588e0004-5081-48d4-bcd9-528afdf2d220%2F27oq3tnb_processed.png&w=3840&q=75)
Transcribed Image Text:B.
V V
1. f(-4)
2. lim f(x)
3. lim f(x)
4. lim f(x)
5. lim f(x)
x-5
![B. LIMITS at INFINITY
Recall your lesson in Piece-wise function.
X→C
In this lesson, you must be able to differentiate between f(c) and lim f(x). In evaluating a function f(c),
when you do DIRECT SUBSTITUTION, the result must be a DEFINED NUMBER (A NUMBER THAT
EXIST), otherwise f(c) is UNDFINED. Contrary to lim f(x), when you do direct substitution, the answer
maybe indeterminate 0/0 but THERE IS A WAY TO EVALUATE THE LIMIT USING MANY
TECHNIQUES, otherwise lim f(x) DOES NOT EXIST.
x→c
X-C
Let us examine the piece-wise function below.
0
1. f(-4)
2. f(-2)
3. f (0)
The function is defined by the equation.
4. f (1)
5. f(2)
6. f (3)
f(x) =
2+7, -4≤x≤-2
-2,
7. f (4)
8. f(7).
-1,
(x-2)²,
x-4
x-7
7
A Self-Regulated Learning Module
2<x< 1
x = 1
1<x< 4
J
FINDING FOR f(c). Let us examine the piece-wise function above. Our goal is to find the following:
4<x<7
x = 7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b193593-6dda-4d9a-96a1-bcbfa3928dc6%2F588e0004-5081-48d4-bcd9-528afdf2d220%2Fz6lwxmi_processed.png&w=3840&q=75)
Transcribed Image Text:B. LIMITS at INFINITY
Recall your lesson in Piece-wise function.
X→C
In this lesson, you must be able to differentiate between f(c) and lim f(x). In evaluating a function f(c),
when you do DIRECT SUBSTITUTION, the result must be a DEFINED NUMBER (A NUMBER THAT
EXIST), otherwise f(c) is UNDFINED. Contrary to lim f(x), when you do direct substitution, the answer
maybe indeterminate 0/0 but THERE IS A WAY TO EVALUATE THE LIMIT USING MANY
TECHNIQUES, otherwise lim f(x) DOES NOT EXIST.
x→c
X-C
Let us examine the piece-wise function below.
0
1. f(-4)
2. f(-2)
3. f (0)
The function is defined by the equation.
4. f (1)
5. f(2)
6. f (3)
f(x) =
2+7, -4≤x≤-2
-2,
7. f (4)
8. f(7).
-1,
(x-2)²,
x-4
x-7
7
A Self-Regulated Learning Module
2<x< 1
x = 1
1<x< 4
J
FINDING FOR f(c). Let us examine the piece-wise function above. Our goal is to find the following:
4<x<7
x = 7
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