Simplify the following asymptotic expression: f(æ) = (2 + 2² + O(x2)) · (1 이미) (1+을 +0(금) 3 x° + + 2x? - (here, the big-O means as x → +∞) Hint: do not be intimidated by the notation! Pretend that O(x) is of the form Cx for some C and likewise with O(1/x²). Multiply just like these are polynomials, then simplify at the end. ) f(x) = x³ + 3æ? + 2æ + O(x) + 0(1) + 0(÷) O f(x) = x° + 3x² + 2x + O(x) ) f(x)= x³ + 3x² + 2x + O(÷) ) f(x) = x° + 3x + O(x) D f(x) 3 = x° + 2x + O(x)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Topic Video
Question
Simplify the following asymptotic expression:
f(æ) = (2 + 2² + O(x2)) · (1
이미) (1+을 +0(금)
3
x° +
+ 2x?
-
(here, the big-O means as x → +∞)
Hint: do not be intimidated by the notation! Pretend that
O(x) is of the form Cx for some C and likewise with
O(1/x²). Multiply just like these are polynomials, then
simplify at the end.
) f(x) = x³ + 3æ? + 2æ + O(x) + 0(1) + 0(÷)
O
f(x) =
x° + 3x² + 2x + O(x)
) f(x)= x³ + 3x² + 2x + O(÷)
) f(x)
= x° + 3x + O(x)
D f(x)
3
= x° + 2x + O(x)
Transcribed Image Text:Simplify the following asymptotic expression: f(æ) = (2 + 2² + O(x2)) · (1 이미) (1+을 +0(금) 3 x° + + 2x? - (here, the big-O means as x → +∞) Hint: do not be intimidated by the notation! Pretend that O(x) is of the form Cx for some C and likewise with O(1/x²). Multiply just like these are polynomials, then simplify at the end. ) f(x) = x³ + 3æ? + 2æ + O(x) + 0(1) + 0(÷) O f(x) = x° + 3x² + 2x + O(x) ) f(x)= x³ + 3x² + 2x + O(÷) ) f(x) = x° + 3x + O(x) D f(x) 3 = x° + 2x + O(x)
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