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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

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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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
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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