ISM_T11_C02_B - Section 2.5 Infinite Limits and Vertical...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 2.5 Infinite Limits and Vertical Asymptotes 93 (d) lim lim xx ı" x 1 (x 1)(x 1) negative negative negative # ±² ± œœ ± _ Š‹ 19. (a) lim 0 Ä! x x x negative # "" " ±œ² œ ± _ (b) 0 x x x positive # " œ_ (c) lim 2 2 0 x2 Ä $ È x ## Î$ "Î$ # ±"Î$ ±"Î$ ± œ ± œ±œ (d) x1 ı x3 # ± # " ±œ± œ ˆ‰ 20. (a) lim (b) lim x x ı# 2x 4 positive 2x 4 negative positive positive # # ±± ²² œ±_ (c) 0 Ä" 2 0 2x 4 2x 4 4 (x 1)(x 1) # ± # ² ²± œ (d) x 2x 4 4 # " ² œ 21. (a) x 2x x (x 2) positive negative (x 2)(x 1) negative negative # $# # ± _ (b) , x 2 x Ä# x 3 x x ( ) x 4 (x 2)(x 1) # # # ± " œ Á (c) , x 2 x x x ( ) x 4 (x 2)(x 1) # # # ± " œ Á (d) , x 2 x x x ( ) x 4 (x 2)(x 1) # # # ± " œ Á (e) x 2x x (x 2) positive negative (x 2)(x 1) negative negative # # ± _ 22. (a) x x 4x x(x )(x 2) x(x ) (4) 8 (x 2)(x ) (x 1) # $ " " # ² ² # # " ± œ œ (b) lim lim lim x x 4x x(x )(x 2) x(x ) negative positive (x 2)(x ) (x 1) negative # $ # ² ² # " ± œ _ (c) x0 Ä x 4x x(x )(x 2) x(x ) negative positive (x 2)(x ) (x 1) negative # $ # ² ² # " ± œ _ (d) 0 x 0 x 4x x(x )(x 2) x(x ) (1)(3) (x 2)(x ) (x 1) # $ # ² ² # " ± œ œ (e) x x x(x ) positive positive negative ±" ²# and x x x(x ) negative positive negative so the function has no limit as x 0. Ä 23. (a) 2 (b) 2 t t ± ± ±œ ± _ _ 3 3 t t "Î$ "Î$ 24. (a) 7 (b) 7 t t ± ± " " t t $Î& $Î& ²œ _ ± _ 25. (a) (b) x x ’“ " " x( x 1 ) x 1 ) 2 2 # Î$ #Î$ #Î$ #Î$ _ _ (c) (d) x x " " x 1 ) x 1 ) 2 2 # Î$ #Î$ #Î$ #Î$ _ _ 26. (a) (b) x x " " x 1 ) x 1 ) 1 1 "Î$ %Î$ "Î$ %Î$ _ ± _ (c) (d) x x " " x 1 ) x 1 ) 1 1 "Î$ %Î$ "Î$ %Î$ ± _ ± _
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
94 Chapter 2 Limits and Continuity 27. y 28. y œœ " " ± ² x1 29. y 30. y " ± ± x4 x3 3 31. y 1 32. y ± # ² 2x 2 x2 x ²" ²² # 33. y
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

ISM_T11_C02_B - Section 2.5 Infinite Limits and Vertical...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online