Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The graph of a function can never cross one of its horizontal asymptotes. b. A rational function f has both lim f(x) = L (where Lis finite) and lim f(x) = x. X18 8118 c. The graph of a function can have any number of vertical asymptotes but at most two horizontal asymptotes. lim x = ∞-∞ = 0 d. lim (x³ -x) = lim x³. X18 X18 818 -
Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The graph of a function can never cross one of its horizontal asymptotes. b. A rational function f has both lim f(x) = L (where Lis finite) and lim f(x) = x. X18 8118 c. The graph of a function can have any number of vertical asymptotes but at most two horizontal asymptotes. lim x = ∞-∞ = 0 d. lim (x³ -x) = lim x³. X18 X18 818 -
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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Transcribed Image Text:Explain why or why not Determine whether the following state-
ments are true and give an explanation or counterexample.
a. The graph of a function can never cross one of its horizontal
asymptotes.
b. A rational function f has both lim f(x) = L (where Lis
finite) and lim f(x) = ∞.
X18
8118
c. The graph of a function can have any number of vertical
asymptotes but at most two horizontal asymptotes.
d. lim (x³
= lim x³.
lim x
810=0
818
818
- x)
-
-
=
-
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