m251test104

# m251test104 - MATH 251 Test I October 1 2004 There are a...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 251 Test I October 1, 2004 There are a total of 4 problems. No calculators are allowed. 1 _______ Name 2 Section 502 (MWF 10:20—11:10) 3. 507 (TR 11:10—12:25) 4. Total __ 1. Given two lines " L1: \$=—1-3t, y=2—t, z=5+t, L22 \$=3+\$, 3/228, Z:-—3+48,} 8,t€R7 (a) show that L1 and L2 are skew lines; (10%) (b) compute the distance between them. (15%) (a) First, not, W» Of A! ‘42,: web) W410.) (—3) -'-l, (1,2,4), Wt, m 0mm «'6 z. WA 1 W . wt —[~;t:3+§ (x Z) ; ~2—6t: é+z\$ 1-1:: ZS -) 2-t’:7,} '+-;+=4 => -¢,—t=lo =2) f=-—7_ =’-> s: ~l-3t~3= “64:2, W557 s: 2,)t=~z 4m 3:“ t=~3+4s, we 06%; 3+(-L)="3++(L) ‘3? 5=§, “- Xv 41ml 1-; 4M Ala-W hm. (lam-5,194 a mm W E? ‘7‘ T: A l‘3 "l I :(‘4-'7-)i +(12,+I)T+ (—é+1)’]::_é€+nf_§i 'é (“+l)+!301'l)r§(}-g): o I. P l 3:: +3” \$5 1“? Hé “15:7 A '— lVl 0K (310)—3, M A; W £52114 f‘vﬁ'IoL/nm): E ~(o(><~3)+:3 («1—0)°-\$(3'+3)= 0, \z-) - ~éx H33 v53=—18+I§:~3. The. 014mm W A. M494; he and WWW 75» Hm». d’ (,3m’7l It) .. __________,___ __,.___ ﬂee)» +13”+(—§)7’ ,J a} o a a- 2. Let n be a. positive integer greater than 2, and 2—11, f(\$1,\$2,~-a\$n) : (\$%+\$g+“'+\$i)T- (a) Show that f satisﬁes the Laplace equation 62f 62f (92f —0, for (xlyx27-Hamn) 82f(x17\$27 ‘ "7xn) Evaluate W. (a) i=l,1,~~',""- 34;_I Z-m 7, 7. 7. 29;.“ 4 ’3 L 1. xi- Q?) (math + +79.) 3;; (m. +---+—xn) = CZ") (m’vr ~ - - +76)? 2x{ ’1 ——‘ ‘ - -—- «mule-wax ..._._| 3X; __."—..‘ ._£_ . z :(z—n) [Uh-"Md? 1—- nxf' (x."+~-- Hm.) ’ ‘ 'L 1,’ n 7— 9 9 2‘il:L+-~'+ i : 4 '2 l 3%: :22; 97‘: M \ -.:L—' 42-“): L 1:. . n '1 " 1 -%-I = _ f- :"i. n X; (‘x."+.--+x..1 (2.. (x + > +x ) ) ) ~ I - “'2': ' L ‘— “12.4.” ; (HM n-(x.‘+--~+x§ —n- (“I +""’"~) ii; = (ii-n) («Hf-MD"? +9113)?“ Lx,"+-..J,x})1 . “J 9") Y! I— .——~ ’5 2. L 1 ii; : (I‘M) 7‘. (Och-u +792) 7' - 7334‘“ Ha +-'~+Xw) "" 2767,, :-(2—n) n 9cm, (991+ v +79%) 2. 3. (a) Let ﬂay) = muggy If (my) 75 (0,0)- Show that lim f (2:, 3;) does not exist. (12%) (\$,y)~>(0,0) (b) Let f( >— ‘W 'f (a: >7é (0 0) \$3 y — + I 7y 7 ' Prove that lim 3:, =0. (27y)—'(0:0)f( y) (You must check the deﬁnition for a limit rigorously by an (5,6)—argument.) (13%) ( a) Aim7 d4 \jwc) we hm L 1. e~ ’96: ‘ {x09 ;L; ~5x‘x x—>o +0 ) if; XL+3x+ x90 x"([4—’§x”) = —\$‘X _ ~\$=0 ’ x90 1+3x" _ 113.0 ‘0. z _- 1‘7— _ + 5— b (1', >2: ‘ M :_ ~ ‘5 :4 jaw + ‘1 ‘1 '1-90 C1311“??? Tao U (Hg) 7+0 4" 6" A“ &%"L€I;) {‘meawbﬂmO allmfft+ww)wcm M97 4/?0’ iULCX'V‘Dk 6/ 51L \$<J (x—o)‘+(j_oy—<\$ .. X 1' - 7.37, _l \ "flix mm: [J42 _ W“ M <1 l (“VI/j"- : _}|x[£ <»}\$:9/} "ELI, “moi/«946%, 4. (a) Let a > 0 be a given constant. Find the tangent plane to the surface 2 = 0,5102 + y2 at the point (1,1,a + 1). What is the name of the surface given in part (a)? (b) Use differentials to compute an approximation value for with 4 decimal place accuracy. (a) 313— : lax '—‘ 24' 3" MW :3 727%:- x:{,‘1'—f; 2L) x:! :2” ‘1“ +087): 3 %:é(éx1+4mxjt 3. X°:[o) ‘36: g ______.__z +([o)l>:i)éao+q.n;\l 1000 ——I0_ 5 24 [9 _ __ﬂ ’1‘” 3m are (8%) (2%) (15%) ...
View Full Document

## This note was uploaded on 07/22/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

### Page1 / 4

m251test104 - MATH 251 Test I October 1 2004 There are a...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online