University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2023
Views:

497

Pages:

3
Author:

GalacticGuru

CALCULUS NFINITE LIMITS NOTES ASSIGNMENT Objectives: ■ Determine infinite limits from the left and from the right. ■ Find and sketch the vertical asymptotes of the graph of а function. lnfinite Limits Let/ Ье the function given Ьу 3/(х- 2). From Figure 1.39 and the tаЫе, you сап see thatf(x) decreases without bound as х approaches 2 from the left, and /(х) increases without bound as х approaches 2 from the right. 6 ➔ 2 -с\ , 3 r- 2 - 1 - ....... -оо 1 "" [ "'➔,· --+ -1 --1 1-1 �,, \ -+ 2- '\:: 1 1 х J(x) 6 [ -61.5 1 -J0 1.9 1.99 -. l.tJJ() -. (XXJ )() 11(\ - t, t ' . >< >< 1 '1(1)--'- r- 2 ') .(Х)() 2 01 :юо � J(.r) incrc:!SC$ and dttre:1 е \\ i tlщu t !)Ottnd ll) х approothe:; 2. Figure 1.39 This behavior is denoted as: 3 lim -Х-+2- Х-2 = -оо and 3 lim -х-+2+ х-2 = оо А limit in which /(х) increases or decreases without bound as х approaches с is called an infinite limit. NOTE: lim f(x) = оо does not mean that the limit exlsts! lt tells you how the limit fails to exist Ьу denoting the unbounded behavior of f(x) asx approaches с. Examples: Determine the limit of each .function shown in the graphs below as х approaches 1 from the left and from the right. ь. а. • . -1j(X)=х-1 1 1 1 -1 : 1 1 1 \,IIW\ {00 У. ➔ ,- : = � -._·. UtJhlIOtJ� D· 2 -1 3 1 jxl=---, (.\ -1 )- • \�.(� )(41..\- t,,::::>

Calculus Infinite Limits Notes Assignment

Calculus Infinite Limits Notes Assignment - Page 3

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