Solutions to Final Exam Ma12, F05

Calculus (With Analytic Geometry)(8th edition)

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: me— Exam fbwmml — Pea/7,005 1. (35 pts.) Find 3x2)- for each y below. a. y=2x3 +5x2+7x+10 417 ; éfil—quo-I- 7 512a b. y =(x4 +5x3 —x2 +9)sinx if! = (ma/nu -7-x) >42“ J K (x*+5x’-X1+7>W7€ _ 5x3 +8x2 +x—2 x4+6x3 +4x—1 (i3 : K/F'Kvlal' /v6?< 4' ‘)<xq‘.LC‘7c3+ 77(4) .. JX 6K3 +5K1+wc—’l)(4v<5+/87<1 +§>j (7611 (73+ 7‘K‘ ))L c.y d. y = sin(\/3x2 +5x+7) -—I 3‘12 " w» J2 (9XL*4K*7)/L (‘K+’;) x 6. 5x23)3 + 2x+xsin(y) = 2005 } c1 - J [OX/y 4' Ext/71 if + Z 4- WG‘j)+ XWQJ) 2:: '7' 0 (ix 133659" 4' wow?) : WIN/95+ 7— *Mm) ckj _ ’((01<:/~73*'1+M’j> 962C (lngM1+--swv‘7> 2. (14 pts.) For each of the following indicate whether the statement is true or false. Assume that all derivatives exist. No work is necessary. a. If f is differentiable at x, then f is continuous at r False (circle one) b. If f is continuous at x, then f is differentiable at x. True ocircle one) c. For any function f, lim f(x) = f(c). True orircle one) (MAW 4W“ “5“” 14C L (S Cbn’lqvww @ 709 d. i—(fg) = . True or circle one) e. —( f + g) = — +— or False (circle one) f. i i =1 True ocircle one) dx g dx dx g. %( f ( g(x)) = f '(g(x)) g '(x). Tr or False (circle one) ’ 3. (32 pts.) Compute the integrals below. 5 4 2 ,1 a.I§-_3x;_§x_-1gx ;8 73-37813 - x (4,0 x b. Jam/5x2 +9dx : “((1 Au [0 c. [(x+1)2J2x—1dx K : 2‘4 P f x: (our 0/7. / S “I/ma‘k :% all-L Au : LX_SQ&1}(M+q) 7. a ( 5 5’1 3/1 #1 u : i u. ’4' Ar q k ‘ 7 Q + é “ + at u )‘l’ 3’ 7/1 I “9,?” 3,1 4. (10 pts.) When a foreign object lodged in the trachea forces a person to cough, the body apparently maximizes the force on this object by maximizing the velocity of the air stream of the cough. In particular, the body does this by contracting the trachea. Suppose that the air stream velocity, v(r), is related to the radius of the trachea, r, by v(r)=(n-—r)r2, SrSn where n is the normal radius of the trachea. < n 7 o > Find the value of the radius (in the interval [n/2, n]) which maximizes the velocity of the air stream. Explain your work/reasoning. Note: It is acceptable to have your optimal value of r expressed in terms of the normal radius value, n. '2 r90 OV‘ V‘: 32 I 3 W (N [51/1th / \/ Cow’Hun» 0k CM/L/ In) J" mofir" 1/111... wxlwm 4‘. V‘: or VD‘NJ.(S>} 5. (10 pts.) Koch’s Snowflake, named after the Swedish mathematician Helge von Koch (1870-1924) is obtained as follows. Given an equilateral triangle, place equilateral triangles on the middle third of each side. Repeat this process. The first four Koch Snowflakes are shown below: If the first snowflake (the equilateral triangle on the left) has sides of length one, then it can be shown that n—l p(n) = perimeter of 11th snowflake = I n—l a(n) = area of nm snowflake = -‘/—§+ M 1-[:4_] 4 20 9 Here, finally, are your questions: a. What can you say about the snowflake perimeter as you continue to repeat this process? That is, tell me about 332M”)? / 4 ““ <1 fl.» : 00 (45 Ill-90’ b. What can you say about the snowflake area as you continue to repeat this process? That is, tell me about lim a(n)? n—wo 2/1»; Eat affleg‘fq) (45%", new 4‘ :Eiriqét) :’-\F3 + w 5’ ...
View Full Document

This homework help was uploaded on 01/22/2008 for the course MATH 123 taught by Professor Johnson during the Fall '06 term at SDSMT.

Page1 / 5

Solutions to Final Exam Ma12, F05 - me— Exam fbwmml —...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online