{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1552 test 3 key

# 1552 test 3 key - Midterm Three Wednesday Goderdzi Pruidze...

This preview shows pages 1–7. 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 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: Midterm Three, Wednesday, April 02, 2008 Goderdzi Pruidze, MATH 1552-002 Name ................ ‘.<.. .Qj .......................................... There are 7 problems on this exam of total 100 points. Point values are indicated in brackets. You must Show all your work to receive credit. Important: scientiﬁc calculators are required. No books, graphic calculators, or notes are allowed on this exam. Please read each question carefully, show all work, and check afterwards that you have answered all of each question correctly. If you need more space to write, you can use the other side ofeach’ page. Good luck! Trigonometric formulas: . si112(:c) = g— (1 — cos(2\$)) o cosz(:c) = (1 + cos(2:1:)) 1 2 4+2: ”:0 00:0 / ' ‘ +i 4f f (,3: 7+X (7L 1 ‘1‘ ‘ L(' 5‘ , w x ‘4 7; r 723 (, 2?) n23 “3/ V’ hﬂ 5" : 5 (,4) C2—- ’/ Z VI‘H 'X n+|:W7 I 6 V‘:o All ’4; W” ’4’)" ":3 w;/ 03— i 5: 00", 37(4) XM “t ”'7' 4/” m; (MIL-{r- ”‘37) D a K A i" /,.)_ 3 (° / 0/ ICI / 4f, -. [f w:7 S’ﬂ‘(—',)' C () CZ Z: v L : ’ ﬂ, (7' A w; ;) (g -- 5‘, ("4)& :1, 3 L7] Problem 2: [10] Calculate the Taylor polynomials T2 (at) and T3(x) centered at x = 4 for the function f(a:) 263\$. "S (9):: eia i 3" , Ia. 4/2‘)':§€ /§((‘/).:3€ (I 3; ( (X); e i/ , (L, £ q .«~ (71:76: ,L [H ),,, £7€ , 4 5‘ ' (W) 2 37a // / I Z In T t&(x):,m>w(@(x_m + *:){x-a) a ‘f ‘ (“A m (z 5 , ’a . a k; (>0: 9 + 3 e (X— 70+ : {#7) F (a (d y ’1 L 87 ’a 3 Wk 6 + Saki/W 9 040+ ”5—04) Problem 3: [10] Find the Maclaurin polynomial T15(:c) of degree 15 for the function f(a:) = 35in(4:c2). ‘ £00 :— 35130 (4):) Zhﬂ J” ~ 2. y :5?) her: 3; 4x4 n» (gm!) '7 2 2n+/ ”‘1 «I . 3>r° {9Xa): 3 Z() [4X) H30 (Zh+})! .3 )3 arm 4"”; : 3g (1 4’ X ”5‘3“ (Zn-H)’ mi 6 emf! :2 Fl) 3 4/ ‘in+2 -,-, X hzo (2n+l)’ 1 ”53’; “l o l l 2 3 L1 LN 91W 9+L’: In“ I , — 2‘ ’3 >( : X “ 2. ( é IO M /8 L§ l j I M Z IQ / f X K X6} )ﬁ X? j X]? ‘ I 5-3 I g M W7\$ H” y 4*“ h ’ I 3’ 52 O / ' 3 g 3.933 ’0 31/ ) fwd-3H L w X >< ~— ”HX - x + . 2’ 7! 'J?‘ * (1)! 3' _ ....... 3__ /-_, 7 _ ~/‘ , * .4/ "f l I 2 2 343-35‘ 0“ £7 X 7 "f, ZX *— S‘X /Q® 73 Problem 4: For the parametric curve a: = In t, y = 2 — t, (a) [10] Find an equation of the tangent line at t : 2. T; :1 x] :: { J, I ’ : ‘76 g. \,"’t 1: 3:32 é ; 1" Z. ,22 __ \ ~——O,; ><~— l0 y’jb " “1 /;< ,, X0) y j)“/ 2) I d y :. » 2x + a) a j :: 2P~él :0 _, ‘ 4,—3.2 1/“ (b) [10] Eliminate the parameter in the parametric equation and express in the form y = f (cc) X a: 1" f’ x (c) [10] Find d2— at t— — 2. (1562 (if ’ ’f) ,i (((>,,.“€::’{' \?> - 1"” jjc/g "’5’“: (AXZ’ ‘ ‘ ’/'- E :1: 46’ >2, “Qi’ﬁ c\><£ 53 x /Q 2-H '- 5 Problem 5: [10] The point P = (—3, —2) is given in rectangular coordinates. Find the polar coordinates P = (7', 0) with 7" > 0 and 0 _<_ 9 < 27r. Round the answer to two decimal places. Problem 6: [15] Write the polar equation of the vertical line x = —5. L I ;-< s? Problem 7: [15] Draw the Cardioid r = 2 — 25in(6). enclosed in the left halfpiane :E g 0. A: O V/ T. y_ Cb V/ 31: L‘N :7: ‘f I we 3 :5: av" X55 1 L {3 _ ‘ i 249, — ,,. r A L 2. 3/“: L 6 # (l ( fzsirmg CJ 9 B 2. 2- ) Find the area inside of this cardioid, Bonus Problem 1: [7] Derive the Maclaurin series for the function f (x) = arctan(:c). Hint: Use the Taylor series expansion of the derivative of f (as) = arctana: . /§ (X); «—-—/" :_ 3“ _' I we 5- ( ) X ‘3" x. 1: £(f‘>_.:. ,1.»- (13K: \$— (4) K2“ Ax [+x’ ma /, N 8104/ h _ r; :: (:j%g(?q°lx,) ”T </’::jf (L') /kf 'f ‘1: I’);¢ 8y,+/ C 5 (( (1,); omit- (o): D 5;) 3° v; 297+) . t/[H3 ,x Bonus Problem 2: [5] Find the length of the path over the given interval: (mﬁ3ﬁ—1L ogtgi g - 5:1 j (/WM 4% X?4):~2{Z X/Kk): éé j (4' D: 3+5” ‘3 ’ (a cm; 1/7696“ _: .V/V‘iJZTTg—ff C t4574 ; {éhﬁ§g_ 5/ .. x . if 3:2...- J elf/F; _é elf : (3 J7: '+& / 5 a '0 < ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

1552 test 3 key - Midterm Three Wednesday Goderdzi Pruidze...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online