This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 117 Midterm # 1 Winter 2011
Feb. 9, 2011 Instructor: G. Wei San/MW; Name All questions have equal points. Show complete work. Continue on the back of
the page if you need more space. Good luck! 1. Show by deﬁnition that the sequence {ﬁﬁil converges to 0. We “we? t 54m V629}_ saw mg i; ,ﬁ/fé W1; MM
5” i.
_...—— ,. ___ i _ ,
[ﬁr 0/ ("i 4) 7;: 4’5 49 > _§€_ w
u,
> ___...
New (L? N:[_ZL:J+I WK“ M24}
5 I r
i? > 35: {JL— we & 2:
z‘" WT
2. Deﬁnef:[—3,0]—>Rby f($)=2£2:3§_2form7é—2 and f(—2)=—5. Isf
continuous at —2? Justify your conclusion.
M .. "w? 1w x)
F! f' 1;,sz ‘
‘2
A '~ % n— .. 
ETHVZ dim ; 2X 3X 2 5 [2X i)(«\"+.&j f
gym ﬁx”) :3 {m (2%)) ; air
We»), )(eZ ‘
9’ / i .' _ . .u
I’m 7L”) " 7W4)! f ’4 5°”“W a»? 02, 3. a). Let S be a set of real numbers and a = sup 5'. Show that, for any 6 > 0,
there is a point m E S such that a — E <m S a. b). Show that there is a sequence {anﬁil from S converging to a.
£1)(?mﬁaﬁé[WW£Mi¢f/1c’yf 2’70
avg «:5 M M: WW I" fie5' me; if v m p are; Wm mé‘fﬁ m £01: //Wee%{é’m§q 191"“ 571'“;ch Mammy {thpaqi 4. a). For a function f : D —> R, and 230 an accumulation point, give the deﬁnition
of lirnmwwcO = L.
b). Show by deﬁnition that 11inan :52 = 4. i3) (11%.?0) 9 (9’70 L‘f' o£[3(",\’g( (5’ K99}, I
[ffx'JILf (f a.) (X1,ch ma; [xvz/ WA?» [X‘fzféf’ (£144.. 5. a). Give the statement of Bolzano—Weierstrass theorem.
b). Show that a. bounded sequence has a convergent subsequence. (Sorry, only
quoting a homework is not enough. Please Show your work.) g“) My éwM vhf?”wa w 4 mf mg“; 44,;
cu [emf woe mwwme FM_ “1% ,QMtée/mgam §aL: as :a whey/kw? “ﬂag :5 deaf/#M. {if ﬂthéfjxyi‘
Cma‘; {at} to “we WWW M a. M, my Bag/333w a r Aer/5 (gm awemwwﬂ
PM, W A {a} Mute a; Awfwﬁﬁn 1L“, V570 I‘ WZ/Aéwicmﬂf [ﬂ~£/ Mi) [wife/{‘51 “£hl’6; mu? [xxW‘s WWI [ex 677%. JW 53% 7AM té ﬂaw, mi ﬁﬁwé[4%,mak) 11$ mpﬂw. ﬂy,“ Mn“? 13! it mé7w¢ W? ﬁA, 3 ...
View
Full Document
 Fall '07
 RickRugangYe

Click to edit the document details