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1 2) Let f (x) = 3+ 4x-8 Find the following: %3D

1 2) Let f (x) = 3+ 4x-8 Find the following: %3D

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

)Let ?(?) = 3 +1
4?−8
Find the following:

a) lim ?(?)
?→2−

b) lim ?(?)
?→2+

c) lim ?(?)
?→2

d) ?(2)


e) lim ?(?)
?→∞

2) Let \( f(x) = 3 + \frac{1}{4x - 8} \) Find the following:
Transcribed Image Text:2) Let \( f(x) = 3 + \frac{1}{4x - 8} \) Find the following:
**Function and Limits Analysis** The following explores the function \( f(x) = \frac{3x - 1}{x - 2} \) and its behavior at different points. **Graph Overview:** - The graph displays the function \( f(x) = \frac{3x - 1}{x - 2} \). - There appears to be a vertical asymptote at \( x = 2 \). - The horizontal asymptote is at \( y = 3 \). **Limit Calculations:** a) \( \lim_{{x \to 2^{-}}} f(x) \) b) \( \lim_{{x \to 2^{+}}} f(x) \) c) \( \lim_{{x \to 2}} f(x) \) d) \( f(2) \) e) \( \lim_{{x \to \infty}} f(x) \)
Transcribed Image Text:**Function and Limits Analysis** The following explores the function \( f(x) = \frac{3x - 1}{x - 2} \) and its behavior at different points. **Graph Overview:** - The graph displays the function \( f(x) = \frac{3x - 1}{x - 2} \). - There appears to be a vertical asymptote at \( x = 2 \). - The horizontal asymptote is at \( y = 3 \). **Limit Calculations:** a) \( \lim_{{x \to 2^{-}}} f(x) \) b) \( \lim_{{x \to 2^{+}}} f(x) \) c) \( \lim_{{x \to 2}} f(x) \) d) \( f(2) \) e) \( \lim_{{x \to \infty}} f(x) \)
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