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25 September, 2013 Exam lB Math 1100 UID: Name: Instructions: • Answer each question in the space provided. • No calculators are allowed. Question Points 1 6 2 8 3 9 4 9 5 8 6 16 7 9 8 10 9 16 10 9 Total: 100 Score Math 1100 25 September, 2013 Exam 1, Page 2 of 11 1. (6 points) Fill in the blanks: (a) A derivative is the slope of the tion at a point. Likf fve’i4 (b) A derivative represents the instantaneous of a function at a point. Ck (c) The derivative of a revenue function represents to a func o ck 5i r I 2. (8 points) Use the graph below to compute each of the following. Write DNE if it does not exist. (a) f (-1) 2 = (b) limx (e) f(2) —1 (f) limx (c) limx —+ —1 (d) limx — —1 = = Q I = 2 = = (g) limx —+ 2 (h) 1im — 2 = —1 I - Math 1100 25 September, 2013 Exam 1, Page 3 of 11 3. (9 points) Determine whether each of the following graphs is continuous at r = 1. If not, explain why not. Your explanation should reference the definition of continuity and/or the three conditions required. (Write your answer to the right of each graph.) (a) (b) PC,’- Coil hvivwS; (c) coil (V i-tx) dc) ex Math 1100 Exam 1, Page 4 of 11 25 September, 2013 4. (9 points) Complite the following limits or state that they do not exist. (a) lim 2x 3 + 2T + 4 x—+ 1 4-Lx3 Z A (b) lim x-*3 33 2+9 x 3 — 0 ex,SI (c) lim jIkt X-4-2 (XfZ)(.i) X—-2 (x) c-z _L1 4 x+2 Exam 1, Page 5 of 11 Math 1100 5. (8 points) Use the definition of a derivative tive of f(x) , LLixh)zJ — (not = 1141 - l1-) - derivative rnles) to compute the deriva 4x + 2 L’L1x.,zJ 1, 4Lk1Z_Cly-Z 25 September. 2013 Exam 1, Page 6 of 11 Math 1100 6. (16 points) Differentiate each function. Use any method you like. (a) — 7 x - 3 7x’*Zx _7 ix + Z - (b) g(x) - (SXL) --1 :x xg 9 1 (continued on next page) x+1 = 32 25 September, 2013 -h t t 9 >c. ii + + II (1’ c1% H II -4 CD CD C.31 I, I’ C CD rj I >< I >€‘ ( “I N I I) i (_, i .rl II !_ ,I I, II N _z N >< CD CD CD U) I. C CD I + I I II Math 1100 Exam 1, Page 9 of 11 25 September, 2013 8. (10 points) Evaluate the following limit. Show your work. Your answer will be a function of x and should be simplified. • 6 —x (+1i) hm Ii h (h)&_c Math 1100 25 September, 2013 Exam 1, Page 10 of 11 9. (16 points) Samantha Carter wants to open a restaurant that serves blue Jell-o. She estimates that her profit in dollars from selling x servings of blue Jell-o will be P(x) For reference: 202 = = 52 +4x — 40 400 (a) What is Carter’s profit on 20 servings of blue Jell-o? P(z (w)’ (zo)-o -Sf- O-Ljt, $35(b) What is Carter’s marginal profit function? )C) - X 20 4-9 (c) What is Carter’s marginal profit at x ‘(2O j-- (u) = 20? 1L1 3.SO (d) Use your answer to part (c) to estimate Carter’s profit from 30 servings of blue Jell-o. P(3o) PftC)i- io.P’(z) . jc- $7Q lOb(3.5) 25 September, 2013 Exam 1, Page 11 of 11 Math 1100 10. (9 points) Colonel O’Neill is flying an X-301 aircraft. Its height in meters aft.er t seconds is given by 2 + 20t + 15 h(t) = 8t (a) How high is Colonel O’Neill aft.er 10 seconds? (1o- uCio) &lOO i- is i-1 (b) ‘vVhat is Colonel O’Neill’s velocity after 10 seconds? e 1(é 4-ZC j ( 1 k(1o) l1toF it) L) vk1/ (c) What is Colonel O’Neill’s acceleration after 10 seconds? “‘e) 1( z (d) (0 points) What do you think would happen if Colonel O’Neill and Samantha Carter teamed up to fight aliens? You may answer in words or pictures. Use the back of this sheet if you need to. y’I41 esld je(i1oI39tC$. 7ltt 1 Co(. We”l1 I4’(biCfIC Fr rroc& al4X h-e 3 h-c ’io 4 ki wovid w1 fky .I%ALAd PM (p eaffh &4p och4.eoI?y)caI ok4 ,po4-vC.’. jy çeverQl -lifits Ii 5 rl1frSh)1 cHk QITt(. yell-c. /j1 -e’° dt7.Ll