CalcNotes0203-page18

CalcNotes0203-page18 - (Section 2.3: Limits and Infinity I)...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
(Section 2.3: Limits and Infinity I) 2.3.18 Solution Method 2 (The “Short Cut”: Dominant Term Substitution) Again, Nx () = 4 x 3 + x ± 1 , and Dx = 5 x 3 ± 2 x . Then, fx = . In our limit analysis, we may replace with its dominant term, 4 x 3 , and we may replace with its dominant term, 5 x 3 . This is justified by the Factoring Principle of Dominance (which also gives rise to a rigorous method, but Solution 1 is probably easier): lim x ±² 4 x 3 + x ³ 1 5 x 3 ³ 2 x = lim x 4 x 3 1 + 1 4 x 2 ³ 1 4 x 3 ´ µ · ¸ ¹ ± 1 ³³ ´ ³³ 5 x 3 1 ³ 2 5 x 2 ´ µ · ¸ ¹
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online