{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

File0006

# File0006 - Section 2.5 Infinite Limits and Vertical...

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

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 ]}