{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

File0006 - Section 2.5 Infinite Limits and Vertical...

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

View Full Document Right Arrow Icon
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Section 2.5 Infinite Limits and Vertical Asymptotes (b) 11m f(x)= x440 x—i Since |x2 — 0| 2 |—x2 if —6 < x < O. liIr(1)_ x 2sin(% ) 2 0 by the sandwich theorem since —2x < x2 sin (%)<x2forallx;£0. 4 0| : x2 < 6 whenever |x| < fl, we choose 6 = fiand obtain |x2 sin (;) — 0| < 6 (C) The function f has limit 0 at x0 = 0 since both the right-hand and left-hand limits exist and equal 0. . . l _ . l . _. '1 CDS‘ _ 83. xilgooxsz—aln’nOgmnO—l, (0“;1) 84. thm 7‘?_61§%‘ 1+ ~ 3x+4 . 3+1 3+4: 3 1 . : m : 1 ~_ 2 _ : _ 85 X11350 2x—5 Xfl‘ioo 2_;5 [5110 2—5: 2’ (I x) . l 1/x_ . z_ _ l 86' lemoo (x) _Z£1_,r%+£ ‘ ’ (2“ ) cos 0 H 1:146:11 87. xiirgoc (3+5) (003%) — 11m0 (3+26)(cos6)= (3)(1)=3 (62%) 88. ximoo (f; — cos %) (1+ sin %) = 913% (392 — cos 6)(1 +sin 19): (0— l)(l +0): ,(9 = i) 2.5 INFINITE LIMITS AND VERTICAL ASYMPTOTES 5 x 11mg. 4 4 —oo (4—) 6- x 12m5- =oo (::.::44:) 9. (a) X11112)+ 331/3 = 00 (b) Xl_i>mO_ 331/3 2 ~00 10. (a) $115+ is :00 (b) x1364 x—f/gz—oo 13. 11m _ tan x z oo 14. lim sec X — oo X46) X4 (77”) 15. 01316‘ (1 +csc 9) 2 — 16. lim (2-cot0)=—ooand lim‘ (2—cot9) t9—>0+ 9-90 1 - 1 _ 17-(a) x132. x»4-x1§g.r+m‘°° ( 1 fl, - 1 __ (b) Kiln? xL4 ’ XE“; (x+2)(x—2) “ 00 ( z 00, so the limit does not exist 1 positive-positive) 1 positive-negative) 71 ...
View Full Document

{[ snackBarMessage ]}