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Exam 1 Key - Calculus I Exam#1 Spring 2011 Name Show all of...

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Unformatted text preview: Calculus I Exam #1 Spring 2011 Name Show all of your work on this paper in the space provided. Solutions without correct supporting work will not earn credit. All answers must be exact unless stated otherwise in the problem. Only your best 10 attempts will count towards your grade. © 1. Use the graph of y = f (x) given below to find the limits indicated. ~2. a. lim f (x) = x—>2' b. lim f(x)= i x—)2‘ c. limf(x)= 9M6— x42 2. Use the graph given in #1 t answer. a. lin31 f (x) = 4 b. x-vaiues where the function is not continuous —-' 2 3 Q I 3 c. x—values where the function 15 not differentiable. ._ a 1 a I 3 J 5 3.. Evaluate without using a graph or table. Note that possible appropriate answers include DNE, 00 and - 00 a. lim(5 a y)% = i (0 b. lim—SJ—c—+—4:—2- = 9% A. x40 x j.” 4. Evaluate without using a graph or table. Note that possible appropriate answers include DNE’W'OO f @ a. lim6cot6 =_’i\'— a. lim i=4; x+1 9—»0 .1r—>1+ ‘m acme __ 9, _ goo Sine rig/“O . e r 9‘5 :: ((3.731— 5. Evaluate without using a graph or table. Note that possible appropriate answers include DNE, 00 and -00 1 1 (.7. 1'90 a. lim + x __ E 9. ) 1). lim 3x4 _ 5x x—rO 3 x-wo 1'- 5x4 :Qizm seam) %'5 >030 axc 21% :"A ,_,i _.___5; Mam/(fl " 5 6. Evaluate without using a graph or table. Note that possible appropriate answers include DNE, 00 and -00 2x 1 + x + sin x —- 00 b.1im————— "" H0 3003): a. lim H 4“ x + 8 7. Find all x-values where the function is discontinuous. Determine if the discontinuities are removable or nonremovable.. a. f (x) = x _; Discontinuous at x = -5 Reason: " 2 I E x + Removable or Nonremovable? Lb b. The definition of continuity states that a fimction y = f (x) is continuous at a point x = a if and only if the following three conditions are met: (Make sure you are very precise and use correct notation.) 8. Find f '(x) using the definition of the derivative: f(x) = 2x2 + x —— 3. Then find the equation of the tangent line to the graph at the point where x = 2. l _ 2 -- '"(ZJLz-i—X'”3 $00.. kg W; -.: ' meme?” "312 to two m:$’(2,):q dangle-'5 1’7 (2,1) — \|-'7:CfX’lg "b ' 9. Find 3-5 for p = Eli—I {use the definition of derivative) [q r ,4 - —— F'g QAWL ( H“) i ’5 M 32 aha/l 23 ‘H N50 h; ~50 PU : M ( mm m- (2 we!) K50 ‘hCZ%+Zh+D(Z%+I : (923+ ahgeyflrfijfigfl‘ “ii W50 h (Z%+Zh+f)(Zg/~H I F : likng (2g,+ ZLL—l'l) (234-13 10. Sketch the graph of a function that satisfies the given conditions. No formulas are required—j ust label the coordinate axes and sketch an appropriate graph. f(2)=1. f(—1)=o, mama, max)” Jig f(x) = ——00, and lim f(x) = 1 x—v—co 11. a. If um,H1 f(x) = 5 ,must f be defined at x=1? No b. If it is, must f(I) =5? NO 0. Can we conclude anything about the values of f at x=1? Explain your answer. No 5 ' -t a, Same-Hm m impaidm FEW ‘M \chQJAL . ...
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