Limit calculations. For each real limit, explain whether it is convergent, divergent to ±∞, or otherwise divergent (not to ±∞). If it is convergent, find the limit. You may use any theorems we have proved in class or on homework. x² - 2x - 3 (a) lim T→3 x+2 I-4 1+3x²2x-3 (b) lim r³-1 (c) lim r+1+ I- - 1 Hint: x³ − 1 = (x − 1)(x² + x + 1).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Please answer the a) ,b) and c)

1.
Limit calculations. For each real limit, explain whether it is
convergent, divergent to to, or otherwise divergent (not to too). If it is
convergent, find the limit. You may use any theorems we have proved in class
or on homework.
(a) lim
T→3
x² - 2x - 3
x + 2
X 4
r3 x² - 2x - 3
(b) lim
x³ - 1
(c) lim
r+1+
X
- 1
Hint: ³-1 = (x − 1)(x² + x + 1).
Transcribed Image Text:1. Limit calculations. For each real limit, explain whether it is convergent, divergent to to, or otherwise divergent (not to too). If it is convergent, find the limit. You may use any theorems we have proved in class or on homework. (a) lim T→3 x² - 2x - 3 x + 2 X 4 r3 x² - 2x - 3 (b) lim x³ - 1 (c) lim r+1+ X - 1 Hint: ³-1 = (x − 1)(x² + x + 1).
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