M408C_Exam1_Solutions

M408C_Exam1_Solutions - Exam 1 Math 4080 Name Fall 2009 TA...

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Unformatted text preview: Exam 1 Math 4080 Name Fall 2009 TA Discussion Time: TTH You must show sufficient work in order to receive full credit for a problem. Do your work on the paper provided. Write your name on this sheet and turn it in with your work. Please write legibly and label the problems clearly. Circle your answers when appropriate. No calculators allowed. 1. Calculate the limits below, if they exist. In the case that a limit doesn’t exist, indicate whether the limit approaches 00. —00, or neither. You must show sufficient work to get credit for a correct answer. 3 2 — 5 — 2 (a) (10 points) 3 (b) (10 points) hm < x 2 > m—>2— l$—21_CL‘—2 1 1 1 10 ' t 1' [—(————)] (CH poms)tl—I>Itit 2+2t 2 2. (10 points) Find all values of a that make the function f below continuous at :r = 1. Justify your answer. a2—2cr, 2721 use): _ ,, asm(—),x<1 2m 3. (10 points) Use the definition of derivative to calculate f’ for f = \/2 — 31‘. (You must use the definition, not the differentiation rules, in order to get credit for this problem.) 4. An object moves along a straight line, its position at time t given by 8(t) = sin2t — cos2 t, 0 S t 3 7r, where s is measured in meters and t in seconds. (a)(10 points) Find all times (if any exist) at which the velocity of the object is 0. (b) (10 points) Find the acceleration of the object when t = % IE2 x/Zm— 1 where the tangent line is horizontal. 5. (10 points) Let y = for at > %, Find all points on the curve (if any exist) d 1 1 6. (10 points) Find d—y if $3; = — + —. Simplify your answer to a reasonable degree. at y a: sec(:c2) 7. (10 points) Find 3/ if y : 2 . Simplify your answer to a reasonable degree. :13 [BONUS ON NEXT 'PfieE] sec :0 — 1 Bonus (5 points): Let f = 1’ (30555 1, J: g 0 Determine whether f is differentiable at :E = 0. Justify your work. ,.I7>0 4 /l/\ T/a/Vv; W” 3‘37‘ ~70 ,___———-—--—-———""“ JA .(a\§, (C (3-3mm) 42-”) W3 Jfl( J-S(X+h) + JAQD m : \/.1— Show) + m )_—Q.$~'1.t Last—amt Lyn) .—_ 43¢;t4‘4t )30 :7 Wtzo (nwarO W%QOWWt;Oln71/” Sec H ax (ZY—l) -—YL (M4)?" 3YZ'2X :O Y(3Y—Z) :0 “‘7X:(3 (AX; (l .9 AL " W - d i M( W x“ M(‘34%\ 3+w3' = '2' ._ _L 5’- X‘ I _L vi 3 +‘3L3: —3 X2. 3! : -gviL ~ _YL‘33._52_ Y+LL “ $52.4"; ...
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M408C_Exam1_Solutions - Exam 1 Math 4080 Name Fall 2009 TA...

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